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BEGIN:VEVENT
SUMMARY:Weiren Zhao (NYU Abu Dhabi)
DTSTART:20200416T131500Z
DTEND:20200416T140500Z
DTSTAMP:20260422T225658Z
UID:IMS/1
DESCRIPTION:Title: Invi
scid damping for a class of monotone shear flow\nby Weiren Zhao (NYU A
bu Dhabi) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this talk\, I
am going to talk about the nonlinear inviscid damping for a class of monot
one shear flows in the finite channel for initial perturbation in Gevrey c
lass with compact support. The main idea of the proof is to use the wave o
perator of a slightly modified Rayleigh operator in a well chosen coordina
te system. This is a joint work with Nader Masmoudi.\n
LOCATION:https://researchseminars.org/talk/IMS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Ros-Oton (Universität Zürich)
DTSTART:20200416T140500Z
DTEND:20200416T145500Z
DTSTAMP:20260422T225658Z
UID:IMS/2
DESCRIPTION:Title: Gene
ric regularity of free boundaries for the obstacle problem\nby Xavier
Ros-Oton (Universität Zürich) as part of PDE seminar via Zoom\n\n\nAbstr
act\nThe obstacle problem is the most classical and motivating example in
the study of free boundary problems. A milestone in this context is the cl
assical work of Caffarelli (Acta Math. 1977)\, in which he established for
the first time the regularity of free boundaries in the obstacle problem\
, outside a certain set of singular points. A long-standing open question
in the field asks to establish generic regularity results in this setting
(e.g. to prove that for ``almost every solution'' there are no singular po
ints). The goal of this talk is to present some new results in this contex
t\, proving in particular the generic regularity of free boundaries for th
e obstacle problem in $\\R^3$. This is a joint work with A. Figalli and J.
Serra.\n
LOCATION:https://researchseminars.org/talk/IMS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hui Yu (Columbia University)
DTSTART:20200416T150000Z
DTEND:20200416T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/3
DESCRIPTION:Title: Regu
larity of the singular set in the fully nonlinear obstacle problem\nby
Hui Yu (Columbia University) as part of PDE seminar via Zoom\n\n\nAbstrac
t\nObstacle problem is one of the well-studied free boundary problems. Whe
n the operator is the Laplacian\, it is known that the free boundary consi
sts of two parts: the regular part and the singular part. The regular part
is an analytic hypersurface\, and the singular part is covered by C1-mani
folds with various dimensions.\n\nWhile the tools for the study of the reg
ular part is robust enough that the theory has been generalized to many ot
her free boundary problems\, up to now all developments on the singular pa
rt rely on monotonicity formulae. Such formulae are only expected for the
Laplacian and linear operators with very regular coefficients. Consequentl
y\, very little is known about the singular set when the operator is not t
he Laplacian.\n\nIn this talk we describe a new method to study the singul
ar set in the obstacle problem. This method does not depend on monotonicit
y formulae and works for fully nonlinear elliptic operators. The result we
get matches the best-known result for the case of Laplacian.\n\nThis is b
ased on joint work with Ovidiu Savin from Columbia University.\n
LOCATION:https://researchseminars.org/talk/IMS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elio Marconi (University of Basel)
DTSTART:20200423T130000Z
DTEND:20200423T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/4
DESCRIPTION:Title: Regu
larity estimates for the flow of BV autonomous divergence-free planar vect
or fields\nby Elio Marconi (University of Basel) as part of PDE semina
r via Zoom\n\n\nAbstract\nWe consider the appropriate notion of flow $X$ a
ssociated to a bounded divergence-free vector field $b$ with bounded varia
tion in the plane. We prove a Lusin-Lipschitz regularity result for $X$ an
d we show that the Lipschitz constant grows at most linearly in time. As a
consequence we deduce that both geometric and analytical mixing have a lo
wer bound of order $1/t$ as $t\\to \\infty$. This is a joint work with Pao
lo Bonicatto.\n
LOCATION:https://researchseminars.org/talk/IMS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Collot (Courant institute of mathematical Sciences)
DTSTART:20200423T140000Z
DTEND:20200423T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/5
DESCRIPTION:Title: On t
he derivation of the homogeneous kinetic wave equation\nby Charles Col
lot (Courant institute of mathematical Sciences) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nThe kinetic wave equation arises in many physical si
tuations: the description of small random surface waves\, or out of equili
bria dynamics for large quantum systems for example. In this talk we are i
nterested in its derivation as an effective equation from the nonlinear Sc
hrodinger equation (NLS) for the microscopic description of a system. More
precisely\, we will consider (NLS) in a weakly nonlinear regime on the to
rus in any dimension greater than two\, and for highly oscillatory random
Gaussian fields as initial data. A conjecture in statistical physics is th
at there exists a kinetic time scale on which\, statistically\, the Fourie
r modes evolve according to the kinetic wave equation. We prove this conje
cture up to an arbitrarily small polynomial loss in a particular regime\,
and obtain a more restricted time scale in other regimes. The main difficu
lty\, that I will comment on\, is that one needs to identify the leading o
rder statistically observable nonlinear effects. This means understanding
correlation between Fourier modes\, and relating randomness with stability
and local well-posedness. The key idea of the analysis is the use of Feyn
man interaction diagrams to understand the solution as colliding linear wa
ves. We use this framework to construct an approximate solution as a trunc
ated series expansion\, and use in addition random matrices tools to obtai
n its nonlinear stability in Bourgain spaces. This is joint work with P. G
ermain.\n
LOCATION:https://researchseminars.org/talk/IMS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20200423T150000Z
DTEND:20200423T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/6
DESCRIPTION:Title: The
power spectrum of passive scalar turbulence in the Batchelor regime\nb
y Jacob Bedrossian (University of Maryland) as part of PDE seminar via Zoo
m\n\n\nAbstract\nIn 1959\, Batchelor predicted that passive scalars advect
ed in fluids at finite Reynolds number with small diffusivity κ should di
splay a |k|−1 power spectrum over a small-scale inertial range in a stat
istically stationary experiment. This prediction has been experimentally a
nd numerically tested extensively in the physics and engineering literatur
e and is a core prediction of passive scalar turbulence. Together with Ale
x Blumenthal and Sam Punshon-Smith\, we have provided the first mathematic
ally rigorous proof of this prediction for a scalar field evolving by adve
ction-diffusion in a fluid governed by the 2D Navier-Stokes equations and
3D hyperviscous Navier-Stokes equations in a periodic box subjected to sto
chastic forcing at arbitrary Reynolds number. These results are proved by
studying the Lagrangian flow map using infinite dimensional extensions of
ideas from random dynamical systems. We prove that the Lagrangian flow has
a positive Lyapunov exponent (Lagrangian chaos) and show how this can be
upgraded to almost sure exponential (universal) mixing of passive scalars
at zero diffusivity and further to uniform-in-diffusivity mixing. This in
turn is a sufficiently precise understanding of the low-to-high frequency
cascade to deduce Batchelor's prediction.\n
LOCATION:https://researchseminars.org/talk/IMS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Barker (École normale supérieure)
DTSTART:20200430T130000Z
DTEND:20200430T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/7
DESCRIPTION:Title: Quan
titative estimates for the Navier-Stokes equations via spatial concentrati
on\nby Tobias Barker (École normale supérieure) as part of PDE semin
ar via Zoom\n\n\nAbstract\nIt remains open as to whether or not the 3D Nav
ier-Stokes equations lose smoothness (`blow-up') in finite time. Starting
from Jean Leray\, many authors provided increasingly refined necessary con
ditions for a finite-time blow-up to occur. The majority of these blow-up
behaviours are formulated in terms of critical or subcritical quantities\,
which are notions relating to the scaling symmetry of the Navier-Stokes e
quations. Very recently\, Tao used a new quantitative approach to infer th
at certain 'slightly supercritical' quantities for the Navier-Stokes equat
ions must become unbounded near a potential blow-up.\n\n\nIn this talk I'l
l discuss a new strategy for proving quantitative bounds for the Navier-St
okes equations\, as well as applications to behaviours near a potential s
ingularity . As a first application\, we prove a new potential blow-up rat
e\, which is optimal for a certain class of potential non-zero backward di
scretely self-similar solutions. As a second application\, we quantify a
conditional qualitative regularity result of Seregin (2012)\, which says t
hat if the critical L_{3} norm of the velocity field is bounded along a se
quence of times tending to time $T$ then no blow-up occurs at time $T$.\n
\n\nThis talk is based upon joint work with Christophe Prange (CNRS\, Univ
ersité de Bordeaux).\n
LOCATION:https://researchseminars.org/talk/IMS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camillo De Lellis (IAS\, Princeton)
DTSTART:20200430T140000Z
DTEND:20200430T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/8
DESCRIPTION:Title: The
oriented Plateau problem and a question of Almgren\nby Camillo De Lell
is (IAS\, Princeton) as part of PDE seminar via Zoom\n\n\nAbstract\nThe Pl
ateau problem\, named by Henry Lebesgue after the Belgian physicist Joseph
Plateau\, consists in finding the surface of least area which spans a giv
en contour.\n\nIn order to tackle such question\, generations of mathemati
cians have investigated the very fundamental notions of ``surface''\, ``bo
undary'' and ``area''\, proposing a variety of different theories. \n\nIn
this talk I will give a brief and intuitive exposition of an approach to t
hese concepts introduced by Federer and Fleming in the 60es after the pio
neering work of De Giorgi in the 50es. I will then discuss an open questio
n relating the shapes of the contour and that of the minimizer\, posed by
Almgren in the early eighties and recently solved in a joint work with Gui
do de Philippis\, Jonas Hirsch and Annalisa Massaccesi.\n
LOCATION:https://researchseminars.org/talk/IMS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Deng (University of Southern California)
DTSTART:20200430T150000Z
DTEND:20200430T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/9
DESCRIPTION:Title: Deri
vation of the wave kinetic equation\nby Yu Deng (University of Souther
n California) as part of PDE seminar via Zoom\n\n\nAbstract\nThe wave turb
ulence theory describes the nonequilibrium statistical mechanics for a lar
ge class of nonlinear dispersive systems. A major goal of this theory is t
o derive the wave kinetic equation\, which predicts the behavior of macros
copic limits of ensemble averages for microscopic interacting systems. Usu
ally this limit happens at a particular "kinetic time scale" in the "weak-
nonlinearity" limit where the number of interacting modes goes to infinity
while the nonlinearity strength goes to zero. For nonlinear Schrodinger e
quations such limits have been derived on a formal level and studied exten
sively since the 1920s\, but a rigorous proof remains open.\n\n\nIn this w
ork\, joint with Zaher Hani\, we provide the first rigorous derivation of
wave kinetic equation\, which reaches the kinetic time scale up to an arbi
trary small power\, in a particular scaling regime for the number of modes
and the strength of nonlinearity. We rely on a robust method\, which can
be extended to other semilinear models\, and possibly also to quasilinear
models (such as water waves).\n
LOCATION:https://researchseminars.org/talk/IMS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Raphael (University of Cambridge)
DTSTART:20200507T130000Z
DTEND:20200507T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/10
DESCRIPTION:Title: On
blow up for the defocusing NLS and three dimensional viscous compressible
fluids\nby Pierre Raphael (University of Cambridge) as part of PDE sem
inar via Zoom\n\n\nAbstract\nGlobal existence and scattering for the defoc
using nonlinear Schrodinger equation is a celebrated result by Ginibre-Vel
o in the early 80’s in the strictly energy sub critical case\, and Bourg
ain in 94 in the energy critical case. In the energy super critical settin
g\, the defocusing energy is conserved and controls the energy norm\, but
this is too weak to conclude to global existence which yet had been conjec
tured by many and confirmed by numerical computations. This is a canonical
super critical problem which typically arises similarily in fluid mechan
ics\, and there global existence is either completely open or a direct co
nsequence of the existence of additional conservation laws. In this talk b
ased on recent joint works with Merle (IHES)\, Rodnianski (Princeton) and
Szeftel (Paris Sorbonne)\, I will describe the construction of newsmooth a
nd finite energy highly oscillatory blow up solutions for the defocusing
NLS in suitable energy super critical regimes\, and explain how these new
bubbles are connected to the also new description of implosion mechanisms
for viscous three dimensional compressible fluids.\n\nHere is the poster o
f this talk: https://www.dropbox.com/s/3pgqawpbjh20g6m/5th%20PDE%20Seminar
.pdf?dl=0\n\nPlease visit our website to get more information: \nhttps://n
guyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guido De Philippis (Courant institute of mathematical Sciences)
DTSTART:20200507T140000Z
DTEND:20200507T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/11
DESCRIPTION:Title: Reg
ularity of the free boundary for the two-phase Bernoulli problem\nby G
uido De Philippis (Courant institute of mathematical Sciences) as part of
PDE seminar via Zoom\n\n\nAbstract\nI will illustrate a recent result obt
ained in collaboration with L. Spolaor and B. Velichkov concerning the r
egularity of the free boundaries in the two phase Bernoulli problems. The
new main point is the analysis of the free boundary close to branch points
\, where we show that it is given by the union of two C^1 graphs. This com
plete the analysis started by Alt Caffarelli Friedman in the 80’s\n\nHer
e is the poster of this talk: https://www.dropbox.com/s/3pgqawpbjh20g6m/5t
h%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get more informa
tion: \nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-
zoom\n
LOCATION:https://researchseminars.org/talk/IMS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:In-Jee Jeong (Korea Institute for Advanced Study (KIAS))
DTSTART:20200514T130000Z
DTEND:20200514T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/12
DESCRIPTION:Title: Wel
l-posedness for the axisymmetric Euler equations\nby In-Jee Jeong (Kor
ea Institute for Advanced Study (KIAS)) as part of PDE seminar via Zoom\n\
n\nAbstract\nThe incompressible Euler equations describe the motion of inv
iscid and volume-preserving fluids. The equations respect rotational symme
tries\, and if one considers initial data which is invariant under all rot
ations fixing an axis\, this property holds for the solution as well. The
resulting axisymmetric Euler equations look rather simple\, but as we shal
l see in this talk\, even the basic question of well-posedness turns out t
o be very delicate.\n\nHere is the poster of this talk: www.dropbox.com/s/
htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0\n\nPlease visit our website t
o get more information: \nhttps://nguyenquochung1241.wixsite.com/qhung/pos
t/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Drivas (Princeton University)
DTSTART:20200514T150000Z
DTEND:20200514T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/13
DESCRIPTION:Title: Qua
sisymmetric plasma equilibria with small forcing\nby Theodore Drivas (
Princeton University) as part of PDE seminar via Zoom\n\n\nAbstract\nQuasi
symmetry is a structural property of a magnetic field which ensures that
charge particles remain well confined within the guiding centre approximat
ion of their motion. Identifying plasma equilibria enjoying this property
is a key part of ongoing attempts to achieve efficient plasma fusion. I wi
ll discuss the construction of toroidal equilibria which achieve quasisymm
etry and are sustained by a small forcing.\n\nHere is the poster of this t
alk: www.dropbox.com/s/htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0\n\nPle
ase visit our website to get more information: \nhttps://nguyenquochung124
1.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (École normale supérieure)
DTSTART:20200521T130000Z
DTEND:20200521T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/14
DESCRIPTION:Title: Fro
m Newton to Boltzmann\, fluctuations and large deviations\nby Isabelle
Gallagher (École normale supérieure) as part of PDE seminar via Zoom\n\
n\nAbstract\nI will report on a recent work\, joint with Th. Bodineau\, L.
Saint-Raymond and S. Simonella\, in which we develop a rigorous theory of
macroscopic fluctuations for a hard sphere gas outside thermal equilibriu
m\, in the Boltzmann-Grad limit : in particular we study deviations from t
he Boltzmann equation (describing the asymptotic dynamics of the empirical
density) and provide\, for short kinetic times\, both a central limit the
orem and large deviation bounds.\n\nHere is the poster of this talk: https
://www.dropbox.com/s/807vg0v0nrmlp2d/PDE%20Seminar%207th.pdf?dl=0\nPlease
visit our website to get more information: nguyenquochung1241.wixsite.com/
qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toan T. Nguyen (Penn State University)
DTSTART:20200528T130000Z
DTEND:20200528T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/15
DESCRIPTION:Title: Lan
dau damping and Plasma echoes\nby Toan T. Nguyen (Penn State Universit
y) as part of PDE seminar via Zoom\n\n\nAbstract\nThe talk presents an ele
mentary proof of the nonlinear Landau damping for analytic and Gevrey data
that was first obtained by Mouhot and Villani and subsequently extended b
y Bedrossian\, Masmoudi\, and Mouhot. The construction of an infinite casc
ade of plasma echoes\, that do not belong to the analytic or Gevrey classe
s\, but do\, nonetheless\, exhibit damping phenomena for large times\, wil
l also be presented. This is a joint work with Emmanuel Grenier (ENS Lyon)
and Igor Rodnianski (Princeton).\n\nHere is the poster of this talk: http
s://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%208th.pdf?dl=0\nPlease
visit our website to get more information: nguyenquochung1241.wixsite.com
/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Emmanuel Jabin (University of Maryland)
DTSTART:20200528T140000Z
DTEND:20200528T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/16
DESCRIPTION:Title: Lar
ge stochastic systems of interacting particles\nby Pierre-Emmanuel Jab
in (University of Maryland) as part of PDE seminar via Zoom\n\n\nAbstract\
nI will present some recent results\, obtained with D. Bresch and Z. Wang\
, on large stochastic many-particle or multi-agent systems. Because such s
ystems are conceptually simple but exhibit a wide range of emerging macros
copic behaviors\, they are now employed in a large variety of applications
from Physics (plasmas\, galaxy formation...) to the Biosciences\, Economy
\, Social Sciences...\n\nThe number of agents or particles is typically qu
ite large\, with 10^{20}-10^{25} particles in many Physics settings for ex
ample and just as many equations. Analytical or numerical studies of such
systems are potentially very complex leading to the key question as to wh
ether it is possible to reduce this complexity\, notably thanks to the not
ion of propagation of chaos (agents remaining almost uncorrelated).\n\nTo
derive this propagation of chaos\, we have introduced a novel analytical m
ethod\, which led to the resolution of two long-standing conjectures:\n\n1
) The quantitative derivation of the 2-dimensional incompressible Navier-S
tokes system from the point vortices dynamics\;\n\n2) The derivation of th
e mean-field limit for attractive singular interactions such as in the Kel
ler-Segel model for chemotaxis and some Coulomb gases.\n\nHere is the post
er of this talk: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%2
08th.pdf?dl=0\nPlease visit our website to get more information: nguyenquo
chung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Ionescu (Princeton University)
DTSTART:20200514T140000Z
DTEND:20200514T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/17
DESCRIPTION:Title: Non
linear stability of vortices and shear flows\nby Alexandru Ionescu (Pr
inceton University) as part of PDE seminar via Zoom\n\n\nAbstract\nI will
talk about some recent work on the nonlinear asymptotic\n\nstability of po
int vortices and monotonic shear flows among solutions of the 2D Euler equ
ations. This is joint work with Hao Jia.\n\nHere is the poster of this tal
k: www.dropbox.com/s/htly5kmdcl2dfw2/PDE%20Seminar%206th.pdf?dl=0\n\nPleas
e visit our website to get more information: \nhttps://nguyenquochung1241.
wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Colombo (Ecole polytechnique fédérale de Lausanne)
DTSTART:20200521T140000Z
DTEND:20200521T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/18
DESCRIPTION:Title: Wea
k solutions of the Navier-Stokes equations may be smooth for a.e. time
\nby Maria Colombo (Ecole polytechnique fédérale de Lausanne) as part of
PDE seminar via Zoom\n\n\nAbstract\nRecently\, Buckmaster and Vicol prove
d non-uniqueness of weak solutions to the Navier-Stokes equations which ha
ve bounded kinetic energy and integrable vorticity. We review the current
developments of the topic\, based on the so called convex integration cons
truction\, and discuss in particular the existence of such solutions\, whi
ch in addition are regular outside a set of times of dimension less than 1
.\n\nHere is the poster of this talk: https://www.dropbox.com/s/807vg0v0nr
mlp2d/PDE%20Seminar%207th.pdf?dl=0\nPlease visit our website to get more i
nformation: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom
\n
LOCATION:https://researchseminars.org/talk/IMS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Didier Bresch (Université Savoie Mont-Blanc)
DTSTART:20200507T150000Z
DTEND:20200507T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/19
DESCRIPTION:Title: On
the stationary compressible Navier-Stokes equations\nby Didier Bresch
(Université Savoie Mont-Blanc) as part of PDE seminar via Zoom\n\n\nAbstr
act\nIn this talk\, I remind known results regarding weak solutions for th
e isotropic stationary compressible Navier-Stokes equations with constant
shear and bulk viscosities. Then I will present how to extend the results
to more general stress tensors including anisotropy and non-local terms.
This seminar is based on joint works with Cosmin Burtea (IMJ Paris 7\, Fra
nce).\n\nHere is the poster of this talk: https://www.dropbox.com/s/3pgqaw
pbjh20g6m/5th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get
more information: \nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-
seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Fischer (Institute of Science and Technology Austria (IST A
ustria))
DTSTART:20200521T150000Z
DTEND:20200521T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/20
DESCRIPTION:Title: Wea
k-strong uniqueness principles for interface evolution problems in fluid m
echanics and geometry\nby Julian Fischer (Institute of Science and Tec
hnology Austria (IST Austria)) as part of PDE seminar via Zoom\n\n\nAbstra
ct\nIn evolution equations for interfaces\, topological changes and geomet
ric singularities occur naturally\, one basic example being the pinchoff o
f liquid droplets. As a consequence\, classical solution concepts for such
PDEs are naturally limited to short-time existence results or particular
initial configurations like perturbations of a steady state. At the same t
ime\, the transition from strong to weak solution concepts for PDEs is pro
ne to incurring unphysical non-uniqueness of solutions. In the absence of
a comparison principle\, the relation between weak solution concepts and s
trong solution concepts for interface evolution problems has remained a mo
stly open question. We establish weak-strong uniqueness principles for two
important interface evolution problems\, namely for planar multiphase mea
n curvature flow and for the evolution of the free boundary between two vi
scous fluids: As long as a classical solution to these evolution problems
exists\, it is also the unique BV solution respectively varifold solution.
In the case of multiphase mean curvature flow\, our construction leads to
a gradient-flow analogue of the notion of calibrations.\n\nBased on joint
works with Sebastian Hensel\, Tim Laux\, and Thilo Simon.\n\nHere is the
poster of this talk: https://www.dropbox.com/s/807vg0v0nrmlp2d/PDE%20Semin
ar%207th.pdf?dl=0\nPlease visit our website to get more information: nguye
nquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Yizhao Hou (California Institute of Technology)
DTSTART:20200528T150000Z
DTEND:20200528T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/21
DESCRIPTION:Title: Rec
ent Progress on Singularity Formation of 3D Euler Equations and Related Mo
dels\nby Thomas Yizhao Hou (California Institute of Technology) as par
t of PDE seminar via Zoom\n\n\nAbstract\nWhether the 3D incompressible Eul
er equations can develop a singularity in finite time from smooth initial
data is one of the most challenging problems in mathematical fluid dynamic
s. We first review the numerical evidence of finite time singularity for 3
D axisymmetric Euler equations by Luo and Hou. The singularity is a ring l
ike singularity that occurs at a stagnation point in the symmetry plane lo
cated at the boundary of the cylinder. We then present a novel method of a
nalysis and prove that the 1D HL model develops finite time self-similar s
ingularity. We also apply this method of analysis to prove finite time sel
f-similar blowup of the original De Gregorio model for some smooth initial
data on the real line with compact support. Self-similar blowup results
for the generalized De Gregorio model for the entire range of parameter on
the real line or on a circle have been obtained for Holder continuous ini
tial data with compact support. Finally\, we report our recent progress in
analyzing the finite time singularity of the axisymmetric 3D Euler equati
ons with initial data considered by Luo and Hou.\n\nHere is the poster of
this talk: https://www.dropbox.com/s/ris7y3bbubt6xhu/PDE%20Seminar%208th.p
df?dl=0\nPlease visit our website to get more information: nguyenquochung1
241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Coti Zelati (Imperial College London)
DTSTART:20200604T130000Z
DTEND:20200604T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/22
DESCRIPTION:Title: Inv
iscid damping and enhanced dissipation in 2d fluids\nby Michele Coti Z
elati (Imperial College London) as part of PDE seminar via Zoom\n\n\nAbstr
act\nWe review some recent results on the asymptotic stability of stationa
ry solutions to the two-dimensional Euler and Navier-Stokes equations of i
ncompressible flows. In many cases\, sharp decay rates for the linearized
problem imply some sort of nonlinear asymptotic stability\, both in the Eu
ler equations (through the so-called inviscid damping) and the Navier-Sto
kes equations (undergoing enhanced dissipation). However\, we will see tha
t in the case of the 2D square periodic domain\, the so-called Kolmogorov
flow exhibits much more complex behavior: in particular\, linear asymptoti
c stability holds\, while nonlinear asymptotic stability is not true even
for analytic perturbations.\n\nHere is the poster of this talk: \nhttps://
www.dropbox.com/s/3ixoc26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0\n\nPlease v
isit our website to get more information: \n\nhttps://nguyenquochung1241.w
ixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Alazard (École Normale Supérieure de Paris-Saclay)
DTSTART:20200604T140000Z
DTEND:20200604T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/23
DESCRIPTION:Title: Ent
ropies of free surface flows in fluid dynamics\nby Thomas Alazard (Éc
ole Normale Supérieure de Paris-Saclay) as part of PDE seminar via Zoom\n
\n\nAbstract\nI will discuss recent works with Didier Bresch\, Nicolas Meu
nier and Didier Smets about the dynamics of a free surface transported by
an incompressible flow obeying Darcy’s law. I will consider the Hele-Sha
w and Mullins-Sekerka equations\, as well as the thin-film and Boussinesq
equations. For these equations\, I will present monotonicity properties of
different natures : maximum principles\, Lyapunov functionals and entropi
es. The analysis is based on exact identities which in turn allow to study
the Cauchy problem for classical solutions in any subcritical Sobolev spa
ces.\n\nHere is the poster of this talk: \nhttps://www.dropbox.com/s/3ixoc
26oxs2tblj/9th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get
more information: \n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/p
de-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phan Thanh Nam (LMU Munich)
DTSTART:20200604T150000Z
DTEND:20200604T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/24
DESCRIPTION:Title: Der
ivation of the Bose-Einstein condensation for trapped bosons\nby Phan
Thanh Nam (LMU Munich) as part of PDE seminar via Zoom\n\nAbstract: TBA\n\
nHere is the poster of this talk: \nhttps://www.dropbox.com/s/3ixoc26oxs2t
blj/9th%20PDE%20Seminar.pdf?dl=0\n\nPlease visit our website to get more i
nformation: \n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-semi
nar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhifei Zhang (Peking university)
DTSTART:20200611T130000Z
DTEND:20200611T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/25
DESCRIPTION:Title: Tra
nsition threshold for the 3D Couette flow in a finite channel\nby Zhif
ei Zhang (Peking university) as part of PDE seminar via Zoom\n\n\nAbstract
\nThe plane Couette flow is linearly stable for any Reynolds number. Howev
er\, it could become nonlinearly unstable and transition to turbulence for
small but finite perturbations at high Reynolds number. This is so-called
Sommerfeld paradox. \nOne resolution of this paradox is to study the tran
sition threshold problem\, which is concerned with how much disturbance wi
ll lead to the instability of the flow and the dependence of disturbance o
n the Reynolds number. In a joint work with Qi Chen and Dongyi Wei\, we sh
owed that if the initial velocity $v_0$ satisfies $\\|v_0-(y\,0\,0)\\|_{H^
2}\\le c_0{Re}^{-1}$ for some $c_0>0$ independent of $Re$\, then the solut
ion of the 3D Navier-Stokes equations is global in time and does not trans
ition away from the Couette flow in the $L^\\infty$ sense\, and rapidly co
nverges to a streak solution for $t\\gtrsim Re^{1/3}$ due to the mixing-en
hanced dissipation effect. This result confirms the transition threshold c
onjecture proposed by Trefethen et al.(Science\, 261(1993)\, 578-584) for
the 3D Couette flow in a finite channel with non-slip boundary condition.\
n\nHere is the poster of this talk:https://www.dropbox.com/s/gxyo8whzqnvco
3h/The%2010th%20PDE%20Seminar.png?dl=0\n\nPlease visit our website to get
more information: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-vi
a-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clément Mouhot (University of Cambridge)
DTSTART:20200611T140000Z
DTEND:20200611T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/26
DESCRIPTION:Title: Uni
fied approach to fluid approximation of linear kinetic equations with heav
y tails\nby Clément Mouhot (University of Cambridge) as part of PDE s
eminar via Zoom\n\n\nAbstract\nThe rigorous fluid approximation of linear
kinetic equations was first obtained in the late 70s when the equilibrium
distribution decays faster than polynomials. In this case the limit is a d
iffusion equation. In the case of heavy tail equilibrium distribution (wit
h infinite variance)\, the first rigorous derivation was obtained in 2011
in my joint paper with Mellet and Mischler\, in the case of scattering ope
rators. The limit shows then anomalous diffusion\; it is governed by a fra
ctional diffusion equation. Lebeau and Puel proved last year the first sim
ilar result for Fokker-Planck operator\, in dimension 1 and assuming that
the equilibrium distribution has finite mass. Fournier and Tardif gave an
alternative probabilistic proof\, more general (covering any dimension and
infinite-mass equilibrium distribution) but non-constructive. We present
a unified quantitative PDE approach that obtains constructively the limit
for Fokker-Planck operators in dimensions greater than 2\, but also recove
rs and unifies the previous works. This is a joint work with Emeric Bouin
(Université Paris-Dauphine).\n\nHere is the poster of this talk: https://
www.dropbox.com/s/gxyo8whzqnvco3h/The%2010th%20PDE%20Seminar.png?dl=0\n\nP
lease visit our website to get more information: nguyenquochung1241.wixsit
e.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silvestre (University of Chicago)
DTSTART:20200611T150000Z
DTEND:20200611T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/27
DESCRIPTION:Title: Reg
ularity estimates for the Boltzmann equation without cutoff\nby Luis S
ilvestre (University of Chicago) as part of PDE seminar via Zoom\n\n\nAbst
ract\nWe study the regularization effect of the inhomogeneous Boltzmann eq
uation without cutoff. We obtain a priori estimates for all derivatives of
the solution depending only on bounds of the hydrodynamic quantities: mas
s density\, energy density and entropy density. As a consequence\, a class
ical solution to the equation may fail to exists after certain time T only
if at least one of these hydrodynamic quantities blows up. Our analysis a
pplies to the case of moderately soft and hard potentials. We use methods
that originated in the study of nonlocal elliptic equations: a weak Harnac
k inequality in the style of De Giorgi\, and a Schauder-type estimate.\n\n
Here is the poster of this talk: www.dropbox.com/s/gxyo8whzqnvco3h/The%201
0th%20PDE%20Seminar.png?dl=0\n\nPlease visit our website to get more infor
mation: nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Engelstein (University of Minnesota)
DTSTART:20200618T140000Z
DTEND:20200618T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/28
DESCRIPTION:Title: An
Epiperimetric Approach to Isolated Singularities\nby Max Engelstein (U
niversity of Minnesota) as part of PDE seminar via Zoom\n\n\nAbstract\nThe
presence of singular points (i.e. points around which the object in quest
ion does not look flat at any scale) is inevitable in most minimization pr
oblems. One fundamental question is whether minimizers have a unique tange
nt object at singular points i.e.\, is the minimizer increasingly well app
roximated by some other minimizing object as we “zoom in” at a singula
r point. This question has been investigated with varying degrees of succe
ss in the settings of minimal surfaces\, harmonic maps and obstacle proble
ms amongst others.\n\nIn this talk\, we will present an uniqueness of blow
ups result for minimizers of the Alt-Caffarelli functional. In particular\
, we prove that the tangent object is unique at isolated singular points i
n the free boundary. Our main tool is a new approach to proving (log-)epip
erimetric inequalities at isolated singularities. This epiperimetric inequ
ality differs from previous ones in that it holds without any additional a
ssumptions on the symmetries of the tangent object.\n\nIf we have time\, w
e will also discuss how this method allows us to recover some uniqueness o
f blow-ups results in the minimal surfaces setting\, particularly those of
Allard-Almgren (’81) and Leon Simon (’83). This is joint work with Lu
ca Spolaor (UCSD) and Bozhidar Velichkov (U. Napoli).\n\nhttps://nguyenquo
chung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20200618T150000Z
DTEND:20200618T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/29
DESCRIPTION:Title: Sta
bility of the Minkowski space for the Einstein-Klein-Gordon system\nby
Benoit Pausader (Brown University) as part of PDE seminar via Zoom\n\n\nA
bstract\nWe consider the Einstein-Klein-Gordon system which models the evo
lution of a Lorentzian metric associated to one of the simplest matter mod
els (the Klein-Gordon equation) and we consider small perturbations which
decay slowly (more slowly than 1/r)\, and show that the spacetime construc
ted are global and converge back to Minkowski through some modified scatte
ring and describe their properties. This is a joint work with A. Ionescu.\
n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\
n
LOCATION:https://researchseminars.org/talk/IMS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Gilles Lemarié-Rieusset (Laboratoire de Mathématiques et
Modélisation d'Évry)
DTSTART:20200625T130000Z
DTEND:20200625T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/30
DESCRIPTION:Title: On
weak solutions of the Navier-Stokes equations with infinite energy\nby
Pierre Gilles Lemarié-Rieusset (Laboratoire de Mathématiques et Modéli
sation d'Évry) as part of PDE seminar via Zoom\n\n\nAbstract\nOne year ag
o\, Bradshaw and Tsai and\, quite independently\, Fernandez and Lemarié-R
ieusset announced results of global existence of weak solutions for the in
compressible Navier-Stokes equations that had poor decay at infinity. In m
y talk\, I will review some issues on the regularity of such solutions (jo
int work with Pedro Fernandez).\n\nhttps://nguyenquochung1241.wixsite.com/
qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert M. Strain (University of Pennsylvania)
DTSTART:20200625T140000Z
DTEND:20200625T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/31
DESCRIPTION:Title: Glo
bal mild solutions of the Landau and non-cutoff Boltzmann equation\nby
Robert M. Strain (University of Pennsylvania) as part of PDE seminar via
Zoom\n\n\nAbstract\nIn this talk we explain a recent proof of the existenc
e of small-amplitude global-in-time unique mild solutions to both the Land
au equation including the Coulomb potential and the Boltzmann equation wit
hout angular cutoff. Since the well-known works (Guo\, 2002) and (Gressm
an-Strain-2011\, AMUXY-2012) on the construction of classical solutions in
smooth Sobolev spaces which in particular are regular in the spatial vari
ables\, it has still remained an open problem to obtain global solutions i
n an $L^\\infty_{x\,v}$ framework\, similar to that in (Guo-2010)\, for th
e Boltzmann equation with cutoff in general bounded domains. \n\n\n\n\nOn
e main difficulty arises from the interaction between the transport operat
or and the velocity-diffusion-type collision operator in the non-cutoff Bo
ltzmann and Landau equations\; another major difficulty is the potential f
ormation of singularities for solutions to the boundary value problem. \n\
n\n\n\nIn this work we introduce a new function space with low regularity
in the spatial variable to treat the problem in cases when the spatial dom
ain is either a torus\, or a finite channel with boundary. For the latter
case\, either the inflow boundary condition or the specular reflection bou
ndary condition is considered. An important property of the function space
is that the $L^\\infty_T L^2_v$ norm\, in velocity and time\, of the dist
ribution function is in the Wiener algebra $A(\\Omega)$ in the spatial va
riables. \n\n\n\n\nBesides the construction of global solutions in these
function spaces\, we additionally study the large-time behavior of solutio
ns for both hard and soft potentials\, and we further justify the property
of propagation of regularity of solutions in the spatial variables. To t
he best of our knowledge these results may be the first ones to provide an
elementary understanding of the existence theories for the Landau or non-
cutoff Boltzmann equations in the situation where the spatial domain has a
physical boundary. \n\n\n\n\nThis is a joint work with Renjun Duan (The
Chinese University of Hong Kong)\, Shuangqian Liu (Jinan University) and S
hota Sakamoto (Tohoku University).\n\nhttps://nguyenquochung1241.wixsite.c
om/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung-Jin Oh (University of California Berkeley)
DTSTART:20200625T150000Z
DTEND:20200625T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/32
DESCRIPTION:Title: On
the Cauchy problem for the Hall magnetohydrodynamics\nby Sung-Jin Oh (
University of California Berkeley) as part of PDE seminar via Zoom\n\n\nAb
stract\nIn this talk\, I will describe a recent series of work with I.-J.
Jeong on the Hall MHD equation without resistivity. This PDE\, first inves
tigated by the applied mathematician M. J. Lighthill\, is a one-fluid desc
ription of magnetized plasmas with a quadratic second-order correction ter
m (Hall current term)\, which takes into account the motion of electrons r
elative to positive ions. Curiously\, we demonstrate the ill(!)posedness o
f the Cauchy problem near the trivial solution\, despite the apparent line
ar stability and conservation of energy. On the other hand\, we identify s
everal regimes in which the Cauchy problem is well-posed\, which not only
includes the original setting that M. J. Lighthill investigated (namely\,
for initial data close to a uniform magnetic field) but also possibly larg
e perturbations thereof. Central to our proofs is the viewpoint that the H
all current term imparts the magnetic field equation with a quasilinear di
spersive character. With such a viewpoint\, the key ill- and well-posednes
s mechanisms can be understood in terms of the properties of the bicharact
eristic flow associated with the appropriate principal symbol.\n\nhttps://
nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20200618T130000Z
DTEND:20200618T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/33
DESCRIPTION:Title: Mul
tilinear Harmonic analysis for nonlinear PDEs with potentials\nby Fabi
o Pusateri (University of Toronto) as part of PDE seminar via Zoom\n\n\nAb
stract\nMotivated by questions on the stability of topological solitons\,
we study some nonlinear dispersive PDEs with large potentials. Our approac
h is based on the distorted Fourier transform and multilinear harmonic ana
lysis in this setting. We will present results in both 1 and 3 dimensions
from a series of joint works with P. Germain\, G. Chen and A. Soffer.\n\nP
lease visit our website to get more information: nguyenquochung1241.wixsit
e.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimiliano Berti (SISSA)
DTSTART:20200702T130000Z
DTEND:20200702T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/34
DESCRIPTION:Title: Lon
g time dynamics of water waves\nby Massimiliano Berti (SISSA) as part
of PDE seminar via Zoom\n\n\nAbstract\nI will present some long time exist
ence results of the solutions of the water waves equations for bidimension
al perfect fluids under space periodic boundary conditions as well as the
existence of small amplitude time quasi-periodic solutions.\n
LOCATION:https://researchseminars.org/talk/IMS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Burq (Institut de Mathématiques d'Orsay)
DTSTART:20200702T140000Z
DTEND:20200702T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/35
DESCRIPTION:Title: Con
trol for wave equations: revisiting the geometric control condition 30 yea
rs later\nby Nicolas Burq (Institut de Mathématiques d'Orsay) as part
of PDE seminar via Zoom\n\n\nAbstract\nFollowing the pioneering work by B
ardos-Lebeau and Rauch\, the property of controllability for the wave equa
tion has been intensively studied\, mainly in a smooth framework (smooth m
etric and smooth domain). In this lecture\, and I shall present some new
results on observability/control for the wave equation with rough coeffici
ents. This question leads to some interesting ODE questions for vector fie
lds with only continuous coefficients.\n\n\nThis is joint work B. Dehman (
Université Tunis El Manar) and J. Le Rousseau (Université Paris 13).\n
LOCATION:https://researchseminars.org/talk/IMS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huy Nguyen (Brown University)
DTSTART:20200702T150000Z
DTEND:20200702T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/36
DESCRIPTION:Title: Pro
of of modulational instability of Stokes waves in deep water\nby Huy N
guyen (Brown University) as part of PDE seminar via Zoom\n\n\nAbstract\nIt
is proven that small-amplitude steady periodic water waves with infinite
depth are unstable with respect to long-wave perturbations. This modulatio
nal instability was first observed more than half a century ago by Benjami
n and Feir.\n\nIt has never been proven rigorously except in the case of f
inite depth. We provide a completely different and self-contained approach
to prove the spectral modulational instability for water waves in both th
e finite and infinite depth cases. Our linearization retains the physical
variables and is compatible with energy estimates for the nonlinear probl
em.\n\n\nThis is joint work with Walter Strauss (Brown University).\n
LOCATION:https://researchseminars.org/talk/IMS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Tolsa (Autonomous University of Barcelona)
DTSTART:20200709T130000Z
DTEND:20200709T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/37
DESCRIPTION:Title: Uni
que continuation at the boundary for harmonic functions\nby Xavier Tol
sa (Autonomous University of Barcelona) as part of PDE seminar via Zoom\n\
n\nAbstract\nIn a work from 1991 Fang-Hua Lin asked the following question
. Let $\\Omega\\subset\\mathbb R^n$ be a Lipschitz domain. Let $u$ be a fu
nction harmonic in $\\Omega$ and continuous in $\\overline \\Omega$ which
vanishes et $\\Sigma \\subset \\partial\\Omega$ and moreover assume that t
he normal derivative $\\partial_\\nu u$ vanishes in a subset of $\\Sigma$
with positive surface measure. Is it true that then $u$ is identically zer
o? \n\nUp to now\, the answer was known to be positive for $C^1$-Dini doma
ins\, by results of Adolfsson-Escauriaza (1997) and Kukavica-Nystrom (1998
). In this talk I will explain a recent work where I show that the result
also holds for Lipschitz domains with small Lipschitz constant\, and thus
in particular for general $C^1$ domains.\n
LOCATION:https://researchseminars.org/talk/IMS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan-Vasile Matioc (University of Regensburg)
DTSTART:20200709T140000Z
DTEND:20200709T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/38
DESCRIPTION:Title: The
Muskat problem in subcritical Lp-Sobolev spaces\nby Bogdan-Vasile Mat
ioc (University of Regensburg) as part of PDE seminar via Zoom\n\n\nAbstra
ct\nThe Muskat problem is a classical mathematical model which describes t
he motion of two immiscible and incompressible Newtonian fluids in an homo
geneous porous medium. The mathematical model posed in the entire plane ca
n be formulated as an evolution equation for the function that parametrize
s the free boundary between the fluids. When neglecting surface tension ef
fects\, the evolution equation is fully nonlinear and nonlocal and it invo
lves singular integral operators defined by kernels that depend nonlinearl
y on the unknown. We prove that the evolution problem is of parabolic type
in the regime where the Rayleigh-Taylor condition is satisfied. Based upo
n this feature we establish the well posedness of the Muskat problem in al
l subcritical Lp-Sobolev spaces together with a parabolic smoothing proper
ty. This is a joint work with Helmut Abels.\n
LOCATION:https://researchseminars.org/talk/IMS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Isett (University of Texas at Austin)
DTSTART:20200709T150000Z
DTEND:20200709T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/39
DESCRIPTION:Title: A P
roof of Onsager’s Conjecture for the Incompressible Euler Equations\
nby Philip Isett (University of Texas at Austin) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nIn an effort to explain how anomalous dissipation of
energy occurs in hydrodynamic turbulence\, Onsager conjectured in 1949 th
at weak solutions to the incompressible Euler equations may fail to exhibi
t conservation of energy if their spatial regularity is below 1/3-Hölder.
I will discuss a proof of this conjecture that shows that there are nonz
ero\, (1/3-\\epsilon)-Hölder Euler flows in 3D that have compact support
in time. The construction is based on a method known as "convex integrati
on\," which has its origins in the work of Nash on isometric embeddings wi
th low codimension and low regularity. A version of this method was first
developed for the incompressible Euler equations by De Lellis and Székel
yhidi to build Hölder-continuous Euler flows that fail to conserve energy
\, and was later improved by Isett and by Buckmaster-De Lellis-Székelyhid
i to obtain further partial results towards Onsager's conjecture. The pro
of of the full conjecture combines convex integration using the “Mikado
flows” introduced by Daneri-Székelyhidi with a new “gluing approximat
ion” technique.The latter technique exploits a special structure in the
linearization of the incompressible Euler equations.\n\nPlease visit the f
ollowing link: https://nguyenquochung1241.wixsite.com/qhung/post/pde-semin
ar-via-zoom to get more information.\n
LOCATION:https://researchseminars.org/talk/IMS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar Lazar (University of Seville)
DTSTART:20200716T130000Z
DTEND:20200716T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/40
DESCRIPTION:Title: On
the Muskat problem with data in critical Sobolev spaces.\nby Omar Laza
r (University of Seville) as part of PDE seminar via Zoom\n\n\nAbstract\nT
he Muskat problem is a nonlinear and nonlocal equation that models the dyn
amics of the interface of two incompressible and immiscible fluids separat
ed by a porous media. I will present a recent global well-posedness result
in critical Sobolev spaces for the 3D Muskat problem that allows the 2D i
nterface to be arbitrarily large in the Lipschitz semi-norm (joint with F.
Gancedo).\n\nPlease visit the following link: \nhttps://nguyenquochung124
1.wixsite.com/qhung/post/pde-seminar-via-zoom\nto get more information.\n
LOCATION:https://researchseminars.org/talk/IMS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Naber (Northwestern University)
DTSTART:20200716T140000Z
DTEND:20200716T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/41
DESCRIPTION:Title: Ric
ci Curvature and Differential Harnack Inequalities on Path Space.\nby
Aaron Naber (Northwestern University) as part of PDE seminar via Zoom\n\n\
nAbstract\nThere has been an observation of late that many analytic estima
tes on manifolds M with lower Ricci curvature bounds have counterparts on
the path space PM of the manifold when there are two sided bounds on Ricci
curvature. We will begin reviewing some of these\, in particular the est
imates of [Nab]\,[Has-Nab] which generalize the Bakry-Emery-Ledoux estimat
es to path space. We will then discuss new results\, which are joint with
Haslhofer and Knofer\, which generalize the Li-Yau differential harnack i
nequalities to the path space\, under the assumption of two sided Ricci cu
rvature bounds. \n\nTo accomplish this\, we will introduce a family of La
place operators on path space PM\, built from finite dimensional traces o
f the Markovian hessian\, which we will review. The differential harnacks
will take the form of differential inequalities for these operators\, and
will recover the classical Li-Yau when applied the simplest functions on
path space\, namely the cylinder functions of one variable.\n
LOCATION:https://researchseminars.org/talk/IMS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Connor Mooney (University of California\, Irvine)
DTSTART:20200716T150000Z
DTEND:20200716T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/42
DESCRIPTION:Title: The
Bernstein problem for elliptic functionals\nby Connor Mooney (Univers
ity of California\, Irvine) as part of PDE seminar via Zoom\n\n\nAbstract\
nThe Bernstein problem asks whether entire minimal graphs in $\\mathbb{R}^
{n+1}$ are necessarily hyperplanes. This problem was completely solved by
the late 1960s in combined works of Bernstein\, Fleming\, De Giorgi\, Almg
ren\, Simons\, and Bombieri-De Giorgi-Giusti. We will discuss the analogue
of this problem for more general elliptic functionals\, and some recent p
rogress in the case n = 6.\n
LOCATION:https://researchseminars.org/talk/IMS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduard Feireisl (Czech Technical University\, Prague)
DTSTART:20200723T130000Z
DTEND:20200723T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/43
DESCRIPTION:Title: Erg
odic theory for energetically open compressible fluid flows\nby Eduard
Feireisl (Czech Technical University\, Prague) as part of PDE seminar via
Zoom\n\n\nAbstract\nThe ergodic hypothesis is examined for energetically
open fluid systems represented by the barotropic Navier--Stokes equations
with general inflow/outflow boundary conditions.\n\nAny globally bounded t
rajectory generates a stationary statistical solution\,\n\nwhich is interp
reted as a stochastic process with continuous trajectories supported by th
e family of weak solutions of the problem. The abstract Birkhoff--Khinchin
theorem is applied to obtain convergence (in expectation and a.s.) of erg
odic averages for any bounded Borel measurable function of state variables
associated to any stationary solution. Finally\, we show that validity of
the ergodic hypothesis is determined by the behavior of entire solutions.
\n\n (joint work with F. Fanelli (Lyon) and M. Hofmanova (Bielefeld))\n
LOCATION:https://researchseminars.org/talk/IMS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuang Miao (Wuhan University)
DTSTART:20200723T140000Z
DTEND:20200723T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/44
DESCRIPTION:Title: On
the free boundary hard phase fluid in Minkowski spacetime\nby Shuang M
iao (Wuhan University) as part of PDE seminar via Zoom\n\n\nAbstract\nI wi
ll discuss a recent work on the free boundary hard phase fluid model with
Minkowski background. The hard phase model is an idealized model for a rel
ativistic fluid where the sound speed approaches the speed of light. This
work consists of two results: First\, we prove the well-posedness of this
model in Sobolev spaces. Second\, we give a rigorous justification of the
non-relativistic limit for this model as the speed of light approaches inf
inity. This is joint work with Sohrab Shahshahani and Sijue Wu.\n
LOCATION:https://researchseminars.org/talk/IMS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (University of California\, Davis)
DTSTART:20200723T150000Z
DTEND:20200723T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/45
DESCRIPTION:Title: Sho
ck Formation for the 3d Euler Equations\nby Steve Shkoller (University
of California\, Davis) as part of PDE seminar via Zoom\n\n\nAbstract\nTog
ether with Tristan Buckmaster and Vlad Vicol\, we give a constructive proo
f of the shock formation process for the 3d Euler equations with vorticity
. Specifically\, we prove that there exist smooth solutions which form a
generic stable shock with explicitly computable blow up time\, location\,
and direction. The cusp-type solution at blow up is obtained by proving st
ability of a generic blowup profile in modulated self-similar variables.
The stability analysis controls the delicate interaction of wave families
using pointwise bounds along Lagrangian trajectories\, geometric vortici
ty structure\, and high-order energy estimates in Sobolev spaces.\n
LOCATION:https://researchseminars.org/talk/IMS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Toumo Kuusi (University of Helsinki)
DTSTART:20200730T130000Z
DTEND:20200730T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/46
DESCRIPTION:Title: Hig
her-order linearization and regularity in nonlinear homogenization\nby
Toumo Kuusi (University of Helsinki) as part of PDE seminar via Zoom\n\n\
nAbstract\nThe analysis of higher-order linearized equations lets us devel
op an incisive large-scale higher regularity theory for solutions of nonli
near elliptic equations in the context of homogenization. We proceed in an
alogy to the role of the Schauder theory in resolving Hilbert’s 19th pro
blem on the regularity of solutions to nonlinear equations with smooth coe
fficients.\n
LOCATION:https://researchseminars.org/talk/IMS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Institute of Technology)
DTSTART:20200730T140000Z
DTEND:20200730T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/47
DESCRIPTION:Title: Agg
regation-diffusion equation: symmetry\, uniqueness and non-uniqueness of s
teady states\nby Yao Yao (Georgia Institute of Technology) as part of
PDE seminar via Zoom\n\n\nAbstract\nThe aggregation-diffusion equation is
a nonlocal PDE driven by two competing effects: local repulsion modeled by
nonlinear diffusion\, and long-range attraction modeled by nonlocal inter
action. I will talk about how this equation arises in modeling the collect
ive motion of cells\, and discuss several qualitative properties of its st
eady states and dynamical solutions. Using continuous Steiner symmetrizati
on techniques\, we show that all steady states are radially symmetric up t
o a translation. (joint work with Carrillo\, Hittmeir and Volzone). In a r
ecent work\, we further investigate whether they are unique within the rad
ial class\, and show that for a given mass\, uniqueness/non-uniqueness of
steady states are determined by the power of the degenerate diffusion\, wi
th the critical power being m = 2. (joint work with Delgadino and Yan.)\n
LOCATION:https://researchseminars.org/talk/IMS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gómez-Serrano (Princeton University)
DTSTART:20200730T150000Z
DTEND:20200730T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/48
DESCRIPTION:Title: Sym
metry in stationary and uniformly rotating solutions of active scalars
\nby Javier Gómez-Serrano (Princeton University) as part of PDE seminar v
ia Zoom\n\n\nAbstract\nIn this talk\, I will discuss a Liouville type theo
rem for stationary or uniformly-rotating solutions of 2D Euler and the sur
face quasi-geostrophic (SQG) equations. The main question we want to addre
ss is whether every stationary/uniformly-rotating solution must\n be radia
lly symmetric\, if the vorticity is compactly supported. Based\n on joint
work with Jaemin Park\, Jia Shi and Yao Yao.\n
LOCATION:https://researchseminars.org/talk/IMS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chanwoo Kim (University of Wisconsin-Madison)
DTSTART:20200820T140000Z
DTEND:20200820T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/49
DESCRIPTION:Title: Inc
ompressible Euler limit from Boltzmann equation with Boundary\nby Chan
woo Kim (University of Wisconsin-Madison) as part of PDE seminar via Zoom\
n\n\nAbstract\nA rigorous derivation of the incompressible Euler equations
with the no-penetration boundary condition from the Boltzmann equation wi
th the diffuse reflection boundary condition has been a challenging open p
roblem. We settle this open question in the affirmative when the initial d
ata of fluid are well-prepared in a real analytic space\, in 3D half space
. As a key of this advance we capture the Navier-Stokes equations satisfyi
ng the no-slip boundary condition\, as an intermediary approximation of th
e Euler equations through a new Hilbert-type expansion of the Boltzmann eq
uation with the diffuse reflection boundary condition. Aiming to justify t
he approximation we establish a novel quantitative $L^p-L^\\infty$ estimat
e of the Boltzmann perturbation around a local Maxwellian of such viscous
approximation\, along with the commutator estimates and the integrability
gain of the hydrodynamic part in various spaces\; we also establish direct
estimates of the Navier-Stokes equations in higher regularity with the ai
d of the initial- boundary and boundary layer weights using a recent Green
’s function approach. The incompressible Euler limit follows as a byprod
uct of our framework.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post
/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tataru (University of California Berkeley)
DTSTART:20200820T150000Z
DTEND:20200820T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/50
DESCRIPTION:Title: Com
pressible Euler with physical vacuum: an Eulerian approach\nby Daniel
Tataru (University of California Berkeley) as part of PDE seminar via Zoom
\n\n\nAbstract\nThe compressible Euler equation with physical vacuum is a
free boundary problem in gas dynamics\, where the moving boundary represe
nts the interface between gas and vacuum states\, with the density decayin
g to zero at the boundary. Such problems have been traditionally studied
using a Lagrangian approach and at high regularity. In this work we propos
e a comprehensive alternative approach\, fully within the Eulerian setting
\, and which leads to sharp results. This is joint work with Mihaela Ifrim
\; the extension of these results to the relativistic case is also joint w
ith Marcelo Disconzi.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post
/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences)
DTSTART:20200827T130000Z
DTEND:20200827T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/51
DESCRIPTION:Title: Mea
n-Field limits for Coulomb-type dynamics\nby Sylvia Serfaty (Courant I
nstitute of Mathematical Sciences) as part of PDE seminar via Zoom\n\n\nAb
stract\nWe consider a system of N particles evolving according to the grad
ient flow of their Coulomb or Riesz interaction\, or a similar conservativ
e flow\, and possible added random diffusion. By Riesz interaction\, we me
an inverse power s of the distance with s between d-2 and d where d denote
s the dimension. We present a convergence result as N tends to infinity to
the expected limiting mean field evolution equation. We also discuss the
derivation of Vlasov-Poisson from newtonian dynamics in the monokinetic ca
se\, as well as related results for Ginzburg-Landau vortex dynamics.\n\nht
tps://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihaela Ifrim (University of Wisconsin-Madison)
DTSTART:20200827T140000Z
DTEND:20200827T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/52
DESCRIPTION:Title: Two
dimensional gravity waves at low regularity I: Energy estimates\nby M
ihaela Ifrim (University of Wisconsin-Madison) as part of PDE seminar via
Zoom\n\n\nAbstract\nThis article represents the first installment of a ser
ies of papers concerned with low regularity solutions for the water wave e
quations in two space dimensions. Our focus here is on sharp cubic energy
estimates. Precisely\, we introduce and develop the techniques to prove a
new class of energy estimates\, which we call \\emph{balanced cubic estima
tes}. This yields a key improvement over the earlier cubic estimates of Hu
nter-Ifrim-Tataru [12]\, while preserving their scale invariant character
and their position-velocity potential holomorphic coordinate formulation.
Even without using any Strichartz estimates\, these results allow us to si
gnificantly lower the Sobolev regularity threshold for local well-posednes
s\, drastically improving earlier results obtained by Alazard-Burq-Zuily [
3\, 4]\, Hunter-Ifrim-Tataru [12] and Ai [2]. This is joint work with Albe
rt Ai and Daniel Tataru.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/p
ost/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Blumenthal (Georgia Institute of Technology)
DTSTART:20200903T130000Z
DTEND:20200903T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/53
DESCRIPTION:Title: Lag
rangian Chaos\, Scalar Mixing\, and passive scalar turbulence for models i
n fluid mechanics\nby Alex Blumenthal (Georgia Institute of Technology
) as part of PDE seminar via Zoom\n\n\nAbstract\nIn models of fluid mechan
ics\, Lagrangian flow $\\phi^t$ on the fluid domain describes the motion o
f a passive particle advected by the fluid. It is anticipated that typical
ly\, Lagrangian flow $\\phi^t$ is chaotic in the sense of (1) sensitivity
with respect to initial conditions and (2) fast mixing of passive scalars
(equivalently $H^{-1}$ decay for passive scalars). I will present joint wo
rk with Jacob Bedrossian (U Maryland) and Sam Punshon-Smith (Brown U) in w
hich we rigorously verify these chaotic properties for various incompressi
ble and stochastically forced fluid models on the periodic box\, including
stochastic 2D Navier-Stokes and hyperviscous 3D Navier-Stokes. I will als
o present our recent application of these result to the study of passive s
calar turbulence in the Batchelor regime\, i.e.\, the steady state of pass
ive scalars in a fluid (at fixed viscosity) attained as molecular diffusiv
ity goes to 0. In this setting\, we are able to prove Batchelor's inverse
power law for the power spectrum\, the passive scalar analogue of Kolmogor
ov's $-4/3$ law for the power spectrum in the inertial range of a turbulen
t 3D fluid.\n\nhttps://nguyenquochung1241.wixsite.com/qhung/post/pde-semin
ar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lannes (Institut de Mathématiques de Bordeaux\, Universit
é de Bordeaux)
DTSTART:20200903T140000Z
DTEND:20200903T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/54
DESCRIPTION:Title: Flo
ating objects and dispersive perturbations of hyperbolic initial boundary
value problems\nby David Lannes (Institut de Mathématiques de Bordeau
x\, Université de Bordeaux) as part of PDE seminar via Zoom\n\n\nAbstrac
t\nWe will show in this talk how some models for the description of the in
teractions of waves with floating structures can be formulated as hyperbol
ic initial boundary value problems or (depending on the model chosen for t
he propagation of the waves)\, dispersive perturbations of such problems.\
n\n\nAfter recalling some classical results on hyperbolic initial boundary
value problems (in particular on the nature of the admissible boundary co
nditions)\, we will explain how the presence of a dispersive perturbation
in the equations drastically changes the nature of the equations. These di
fferent behaviors raise several questions\, one of which being nature of t
he dispersionless limit. We will show that the presence of dispersive boun
dary layers make this limit singular\, and explain how to control them on
an example motivated by a model for wave-structure interactions.\n
LOCATION:https://researchseminars.org/talk/IMS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Vega (BCAM - Basque Center for Applied Mathematics)
DTSTART:20200910T130000Z
DTEND:20200910T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/55
DESCRIPTION:Title: The
Vortex Filament Equation\, the Talbot effect\, and non-circular jets\
nby Luis Vega (BCAM - Basque Center for Applied Mathematics) as part of PD
E seminar via Zoom\n\n\nAbstract\nWe will propose the vortex filament equa
tion as a possible toy model for turbulence\, in particular because of its
striking similarity to the dynamics of non-circular jets. This similarity
implies the existence of some type of Talbot effect due to the interactio
n of non-linear waves that propagate along the filament. Another consequen
ce of this interaction is the existence of a new class of multi-fractal se
ts that can be seen as a generalization of the graph of Riemann’s non-di
fferentiable function. Theoretical and numerical arguments about the trans
fer of energy will be also given. This a joint work with V. Banica and F.
de la Hoz.\n
LOCATION:https://researchseminars.org/talk/IMS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joachim Krieger (Ecole polytechnique fédérale de Lausanne (EPFL)
)
DTSTART:20200910T140000Z
DTEND:20200910T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/56
DESCRIPTION:Title: Sta
bility of critical Wave Maps blow up beyond the co-rotational setting\
nby Joachim Krieger (Ecole polytechnique fédérale de Lausanne (EPFL)) as
part of PDE seminar via Zoom\n\n\nAbstract\nI will discuss recent work by
Miao\, Schlag and myself which establishes a strong stability (and in fac
t rigidity) result for certain of the blow up solutions for critical Wave
Maps mapping into the sphere constructed by K.-Schlag-Tataru. The result i
s consistent with work by Duyckaerts-Jia-Kenig-Merle\, and the methods are
presumably of much wider applicability.\n\nhttps://nguyenquochung1241.wix
site.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rousset (Université Paris-Sud)
DTSTART:20200917T130000Z
DTEND:20200917T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/57
DESCRIPTION:by Frédéric Rousset (Université Paris-Sud) as part of PDE s
eminar via Zoom\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IMS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Germain (Courant Institute of Mathematical Sciences)
DTSTART:20200917T140000Z
DTEND:20200917T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/58
DESCRIPTION:Title: Vor
tex filament solutions for the Navier-Stokes equations\nby Pierre Germ
ain (Courant Institute of Mathematical Sciences) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nI will present a construction of solutions of the Na
vier-Stokes equations for data whose vorticity are concentrated on 1D curv
es (as measures). This corresponds to large locally self-similar data\, fo
r which the usual perturbative approach to local well-posedness does not a
pply\, and for which a number of interesting questions arise. These data a
re also of fundamental importance from a physical perspective\, since vort
ex filaments are expected to play a crucial role in 3D flows.\n
LOCATION:https://researchseminars.org/talk/IMS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Holden (Norwegian University of Science and Technology)
DTSTART:20200924T130000Z
DTEND:20200924T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/59
DESCRIPTION:Title: A L
ipschitz metric for the Camassa-Holm equation\nby Helge Holden (Norweg
ian University of Science and Technology) as part of PDE seminar via Zoom\
n\n\nAbstract\nThe Camassa—Holm equation\n\n$$\n\nu_t+uu_x+p_x=0\, \\qua
d p-p_{xx}= u^2+1/2 u_x^2\n\n$$\n\nhas received considerable attention si
nce it was first studied by Camassa and Holm in 1993. Part of the interest
stems from the fact that the solution develops singularities in finite ti
me while keeping the $H^1$ norm finite. At wave breaking uniqueness is lo
st as the there are infinitely many ways to extend the solution beyond wav
e breaking. We study the so-called conservative solutions and show how to
construct a Lipschitz metric comparing two conservative solutions.\n\n\nTh
is is joint work with J. A. Carrillo (Imperial) and K. Grunert (NTNU).\n\n
https://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Dodson (Johns Hopkins University)
DTSTART:20200924T140000Z
DTEND:20200924T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/60
DESCRIPTION:Title: Glo
bal well-posedness for the cubic NLS with data in a critical Sobolev space
\nby Benjamin Dodson (Johns Hopkins University) as part of PDE seminar
via Zoom\n\n\nAbstract\nIn this talk discuss global well-posedness for th
e cubic nonlinear Schrodinger equation with initial data in a critical Sob
olev space. We do not require any symmetry on the initial data. The proof
uses decomposition into a finite energy part and a free solution part.\n
LOCATION:https://researchseminars.org/talk/IMS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (Institute for Advanced Study\, Princeton)
DTSTART:20201001T140000Z
DTEND:20201001T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/61
DESCRIPTION:Title: Sur
vey on decoupling\nby Hong Wang (Institute for Advanced Study\, Prince
ton) as part of PDE seminar via Zoom\n\n\nAbstract\nIn 2014\, Bourgain and
Demeter proved the $l^2$--decoupling conjecture for the paraboloid\, whic
h leads to many developments in harmonic analysis. We are going to discuss
some ideas of decoupling and how people use them.\n
LOCATION:https://researchseminars.org/talk/IMS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University)
DTSTART:20201001T150000Z
DTEND:20201001T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/62
DESCRIPTION:by Eugenia Malinnikova (Stanford University) as part of PDE se
minar via Zoom\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IMS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea R. Nahmod (University of Massachusetts)
DTSTART:20201008T130000Z
DTEND:20201008T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/63
DESCRIPTION:Title: Inv
ariant Gibbs measures and global strong solutions for periodic 2D nonlinea
r Schrödinger equations.\nby Andrea R. Nahmod (University of Massachu
setts) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this talk we will
first give a quick background overview of Bourgain's approach to prove th
e invariance of the Gibbs measure for the periodic cubic nonlinear Schrodi
nger equation in 2D and of Gubinelli-Imkeller and Perkowski's para-control
led calculus for parabolic stochastic equations. \nWe will then present ou
r resolution of the long-standing problem of proving almost sure global we
ll-posedness (i.e. existence with uniqueness) for the periodic nonlinear
Schrödinger equation (NLS) in 2D on the support of the Gibbs measure\, fo
r any (defocusing and renormalized) odd power nonlinearity. Consequently w
e get the invariance of the Gibbs measure. This is achieved by a new metho
d we call random averaging operators which precisely captures the intrinsi
c randomness structure of the problematic high-low frequency interactions
at the heart of this NLS problem. \n\n\nThis is joint work with Yu Deng (U
SC) and Haitian Yue (USC).\n
LOCATION:https://researchseminars.org/talk/IMS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-marc DELORT (Université Paris 13)
DTSTART:20201008T140000Z
DTEND:20201008T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/64
DESCRIPTION:Title: Lon
g time dispersive estimates for perturbations of a kink solution of one di
mensional cubic wave equations.\nby Jean-marc DELORT (Université Pari
s 13) as part of PDE seminar via Zoom\n\n\nAbstract\nA kink is a stationar
y solution to a cubic one dimensional wave equation $(\\partial_t^2-\\part
ial_x^2)\\phi =\\phi-\\phi^3$ that has different limits when $x$ goes to $
-\\infty$ and $+\\infty$\, like $H(x) =\\tanh(x/\\sqrt{2})$. Asymptotic\n\
nstability of this solution under small odd perturbation in the energy s
pace has been studied in a recent work of Kowalczyk\, Martel and Mu\\~noz.
They have been able to show that the perturbation may be written as the s
um $a(t)Y(x) +\\psi(t\,x)$\, where $Y$ is a function in Schwartz space\, $
a(t)$ a function of time having some decay properties at\n\ninfinity\, and
$\\psi(t\,x)$ satisfies some local in space dispersive estimate.\n\n\nThe
main result in this talk gives\, for small odd perturbations of the kink
that are\n\nsmooth enough and have some space decay\, explicit rates of d
ecay for $a(t)$ and for $\\psi(t\,x)$ in the whole space-time domain inter
sected by a strip $\\abs{t}\\leq \\epsilon^{-4+c}$\, for any $c>0$\, where
$\\epsilon$ is the size of the initial\n\nperturbation. \n\n\nThis is joi
nt work with Nader Masmoudi.\n
LOCATION:https://researchseminars.org/talk/IMS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grenier Emmanuel (ENS de Lyon)
DTSTART:20201022T130000Z
DTEND:20201022T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/65
DESCRIPTION:Title: On
the instability of viscous boundary layers\nby Grenier Emmanuel (ENS d
e Lyon) as part of PDE seminar via Zoom\n\n\nAbstract\nPrandtl boundary la
yers appear when we study the Navier Stokes equations near a boundary as t
he viscosity goes to zero. The aim of this talk is to review some recents
on the instability of such layers (joint work with Y. Guo and T. Nguyen)\n
LOCATION:https://researchseminars.org/talk/IMS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Gérard (Université Paris-Saclay)
DTSTART:20201022T140000Z
DTEND:20201022T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/66
DESCRIPTION:Title: Int
egrability of the Benjamin--Ono equation and applications\nby Patrick
Gérard (Université Paris-Saclay) as part of PDE seminar via Zoom\n\n\nAb
stract\nI will review recent results about the dynamics of the Benjamin--O
no equation on the torus : sharp wellposedness in the Sobolev spaces\, alm
ost periodicity of solutions\, stability of traveling waves\, existence o
f singular time periodic solutions. All these results are obtained as cons
equences of the construction of a nonlinear Fourier transformation which
is inherited from the Lax pair structure of the equation. I will sketch t
he construction of this transformation and discuss work in progress about
it.\n\nThis talk is based on a series of joint works with Thomas Kappeler
(Zuerich) and Peter Topalov (Boston).\n
LOCATION:https://researchseminars.org/talk/IMS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Visan (University of California\, Los Angeles.)
DTSTART:20201029T150000Z
DTEND:20201029T155000Z
DTSTAMP:20260422T225658Z
UID:IMS/67
DESCRIPTION:Title: Rec
ent progress on well-posedness for integrable PDE\nby Monica Visan (Un
iversity of California\, Los Angeles.) as part of PDE seminar via Zoom\n\n
\nAbstract\nI will present the new method developed in joint work with Kil
lip for proving optimal well-posedness for integrable PDE. I will first d
iscuss this method in the context of the Korteweg-de Vries equation. I wi
ll then discuss subsequent developments (joint with Harrop-Griffiths and K
illip) that have led to optimal well-posedness results for the integrable
nonlinear Schrodinger and the modified Korteweg-de Vries equations.\n
LOCATION:https://researchseminars.org/talk/IMS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Figalli (ETH Zurich)
DTSTART:20201105T140000Z
DTEND:20201105T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/68
DESCRIPTION:Title: Sta
ble solutions to semilinear elliptic equations\nby Alessio Figalli (ET
H Zurich) as part of PDE seminar via Zoom\n\n\nAbstract\nStable solutions
to semilinear elliptic PDEs appear in several problems. It is known since
the 1970’s that\, in dimension n > 9\, there exist singular stable solut
ions. In this talk I will describe a recent work with Cabr\\'e\, Ros-Oton\
, and Serra\, where we prove that stable solutions in dimension n ≤ 9 ar
e smooth. This answers also a famous open problem posed by Brezis\, concer
ning the regularity of extremal solutions to the Gelfand problem.\n
LOCATION:https://researchseminars.org/talk/IMS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renjun Duan (The Chinese University of Hong Kong)
DTSTART:20201112T130000Z
DTEND:20201112T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/69
DESCRIPTION:Title: The
Boltzmann equation for uniform shear flow\nby Renjun Duan (The Chines
e University of Hong Kong) as part of PDE seminar via Zoom\n\n\nAbstract\n
The uniform shear flow for the rarefied gas is governed by the time-depend
ent spatially homogeneous Boltzmann equation with a linear shear force. Th
e main feature of such flow is that the temperature may increase in time d
ue to the shearing motion that induces viscous heat and the system becomes
far from equilibrium. For Maxwell molecules\, we establish the unique exi
stence\, regularity\, shear-rate-dependent structure and non-negativity of
self-similar profiles for any small shear rate. The non-negativity is jus
tified through the large time asymptotic stability even in spatially inhom
ogeneous perturbation framework\, and the exponential rates of convergence
are also obtained with the size proportional to the second order shear ra
te. The analysis supports the numerical result that the self-similar profi
le admits an algebraic high-velocity tail that is the key difficulty to ov
ercome in the proof. This work is joint with Shuangqian Liu.\n
LOCATION:https://researchseminars.org/talk/IMS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Merle (Université de Cergy Pontoise and IHES)
DTSTART:20201119T130000Z
DTEND:20201119T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/70
DESCRIPTION:Title: On
the implosion of a three dimensional compressible fluid\nby Frank Merl
e (Université de Cergy Pontoise and IHES) as part of PDE seminar via Zoom
\n\n\nAbstract\nWe consider the compressible three dimensional Navier Stok
es and Euler equations. In a suitable regime of barotropic laws\, we const
ruct a set of finite energy smooth initial data for which the correspondin
g solutions to both equations implode (with infinite density) at a later t
ime at a point\, and completely describe the associated formation of singu
larity.\n
LOCATION:https://researchseminars.org/talk/IMS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Constantin (Princeton University)
DTSTART:20201203T130000Z
DTEND:20201203T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/71
DESCRIPTION:Title: On
the Nernst-Planck-Navier-Stokes Equations\nby Peter Constantin (Prince
ton University) as part of PDE seminar via Zoom\n\n\nAbstract\nWe review r
ecent results concerning the NPNS system in 2D and 3D.\n\nThe main results
are global stability and regularity results in 2D\, strong nonlinear stab
ility of Boltzmann states in 3D and unconditional global existence and reg
ularity in 3D for large data for the NP-Stokes equations\, and conditional
on regularity of velocity for NPNS\, in the\n\nspecific case of two ionic
species with arbitrary diffusivities and the case of N ionic species with
equal diffusivities. We obtain interior electroneutrality in the limit of
vanishing Debye length in the stable cases.\n\n\nThis is joint work with
M. Ignatova and F-N. Lee.\n
LOCATION:https://researchseminars.org/talk/IMS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose A. Carrillo (University of Oxford)
DTSTART:20210107T140000Z
DTEND:20210107T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/72
DESCRIPTION:Title: The
Landau equation: Particle Methods & Gradient Flow Structure\nby Jose
A. Carrillo (University of Oxford) as part of PDE seminar via Zoom\n\n\nAb
stract\nThe Landau equation introduced by Landau in the 1930's is an impor
tant partial differential equation in kinetic theory. It gives a descripti
on of colliding particles in plasma physics\, and it can be formally deriv
ed as a limit of the Boltzmann equation where grazing collisions are domin
ant. The purpose of this talk is to propose a new perspective inspired fro
m gradient flows for weak solutions of the Landau equation\, which is in a
nalogy with the relationship of the heat equation and the 2-Wasserstein me
tric gradient flow of the Boltzmann entropy. Moreover\, we aim at using th
is interpretation to derive a deterministic particle method to solve effic
iently the Landau equation. Our deterministic particle scheme preserves al
l the conserved quantities at the semidiscrete level for the regularized L
andau equation and that is entropy decreasing. We will illustrate the perf
ormance of these schemes with efficient computations using treecode approa
ches borrowed from multipole expansion methods for the 3D relevant Coulomb
case. From the theoretical viewpoint\, we use the theory of metric measur
e spaces for the Landau equation by introducing a bespoke Landau distance
$d_L$. Moreover\, we show for a regularized version of the Landau equation
that we can construct gradient flow solutions\, curves of maximal slope\,
via the corresponding variational scheme. The main result obtained for th
e Landau equation shows that the chain rule can be rigorously proved for t
he grazing continuity equation\, this implies that H-solutions with certai
n apriori estimates on moments and entropy dissipation are equivalent to g
radient flow solutions of the Landau equation. We crucially make use of es
timates on Fisher information-like quantities in terms of the Landau entro
py dissipation developed by Desvillettes.\n
LOCATION:https://researchseminars.org/talk/IMS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (University of Wisconsin-Madison)
DTSTART:20201217T140000Z
DTEND:20201217T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/73
DESCRIPTION:Title: Lp
improving bounds for spherical maximal operators\nby Andreas Seeger (U
niversity of Wisconsin-Madison) as part of PDE seminar via Zoom\n\n\nAbstr
act\nConsider maximal operators for spherical means where the dilations ar
e\n\nrestricted to a given subset of a compact interval. We discuss Lp imp
roving\n\nestimates for such operators and connections to related global p
roblems.\n\nThe results depend on various notions of fractal dimension of
the dilation\n\nset or subsets of it. There are some unexpected results on
the shape of the\n\npossible type set. This is joint work with Joris Roos
\, and also relates to earlier work with\n\nTheresa Anderson\, Kevin Hughe
s and Joris Roos.\n
LOCATION:https://researchseminars.org/talk/IMS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Gancedo (University of Seville)
DTSTART:20210114T130000Z
DTEND:20210114T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/74
DESCRIPTION:Title: Two
global-in-time results for Muskat\nby Francisco Gancedo (University o
f Seville) as part of PDE seminar via Zoom\n\n\nAbstract\nIn this talk we
consider the Muskat problem\, modeling the dynamics of two incompressible
immiscible fluids in porous media. First\, we consider fluids of different
densities. This case has been extensively studied recently\, in particula
r because its very interesting features. The fluids can be stable\, enter
into unstable regime and next to develop finite time singularities. We sho
w that this scenario is not possible in 3D for arbitrary slope and small d
ata\, providing global-in-time critical solutions. Second\, we deal with c
apillarity forces with viscosity-density fluids. This case is fundamental
in order to understand fingering phenomena. For gravity unstable situation
s\, we show that 2D bubbles exist for all time for initial data given by a
wide balance between small norm\, density\, viscosity and surface tension
.\n
LOCATION:https://researchseminars.org/talk/IMS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Cameron (Courant Institute\, NYU)
DTSTART:20210121T130000Z
DTEND:20210121T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/75
DESCRIPTION:Title: Glo
bal Existence for the 3D Muskat problem\nby Stephen Cameron (Courant I
nstitute\, NYU) as part of PDE seminar via Zoom\n\n\nAbstract\nThe Muskat
problem studies the evolution of the interface between two incompressible\
, immiscible fluids in a porous media. In the case that the fluids have e
qual viscosity and the interface is graphical\, this system reduces to a s
ingle nonlinear\, nonlocal parabolic equation for the parametrization. Ev
en in this stable regime\, wave turning can occur leading to finite time b
lowup for the slope of the interface. Before that blowup though\, we prov
e that an imperfect comparison principle still holds. Using this\, we are
able to show that solutions exist for all time so long as either the init
ial slope is not too large\, or the slope stays bounded for a sufficiently
long time.\n
LOCATION:https://researchseminars.org/talk/IMS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS\, Princeton)
DTSTART:20210311T140000Z
DTEND:20210311T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/76
DESCRIPTION:Title: Loc
al smoothing for the wave equation in 2+1 dimensions\nby Ruixiang Zhan
g (IAS\, Princeton) as part of PDE seminar via Zoom\n\n\nAbstract\nSogge's
local smoothing conjecture for the wave equation predicts that the local
L^p space-time estimate gains a fractional derivative of order almost 1/p
compared to the fixed time L^p estimates\, when p>2n/(n-1). Jointly with L
arry Guth and Hong Wang\, we recently proved the conjecture in R^{2+1}. I
will talk about our proof and explain several important ingredients such a
s induction on scales and an incidence type theorem.\n
LOCATION:https://researchseminars.org/talk/IMS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna L. Mazzucato (Penn State University)
DTSTART:20210325T130000Z
DTEND:20210325T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/77
DESCRIPTION:Title: Mix
ing\, irregular transport\, and enhanced dissipation\nby Anna L. Mazzu
cato (Penn State University) as part of PDE seminar via Zoom\n\n\nAbstract
\nI will discuss transport of passive scalars by incompressible flows and
measures of optimal mixing and stirring. I will give two applications \, o
ne is an example of complete loss of regularity for solution to linear tra
nsport equations\, the others is a global existence result for the advecti
ve Kuramoto-Sivashinsky equation in 2 space dimensions.\n
LOCATION:https://researchseminars.org/talk/IMS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David M. Ambrose (Drexel University)
DTSTART:20210408T130000Z
DTEND:20210408T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/78
DESCRIPTION:Title: Glo
bal existence results for the 2D Kuramoto-Sivashinsky equation\nby Dav
id M. Ambrose (Drexel University) as part of PDE seminar via Zoom\n\n\nAbs
tract\nThe Kuramoto-Sivashinsky equation is a model for the motion of flam
e fronts. In one spatial dimension much is understood\, including that so
lutions exist for all time. Analagous results in two dimensions are much
more limited\; most results in 2D assume that the domain is "thin\," or ap
proximately one-dimensional. We will give an overview of the results in o
ne dimension and of anisotropic results in two dimensions. We will then s
how some global existence theorems for small data in two dimensions withou
t making use of any anisotropy. This includes joint work with Anna Mazzuc
ato.\n
LOCATION:https://researchseminars.org/talk/IMS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Yan Li (Rutgers University)
DTSTART:20210506T140000Z
DTEND:20210506T145000Z
DTSTAMP:20260422T225658Z
UID:IMS/79
DESCRIPTION:Title: Reg
ular solutions of the stationary Navier-Stokes equations on high dimension
al Euclidean space\nby Yan Yan Li (Rutgers University) as part of PDE
seminar via Zoom\n\n\nAbstract\nWe study the existence of regular solution
s of the incompressible stationary Navier-Stokes equations in n-dimensiona
l Euclidean space with a given bounded external force of compact support.
In dimensions $n\\le 5$\, the existence of such solutions was known. In th
is paper\, we extend it to dimensions $n\\le 15$. This is a joint work
with Zhuolun Yang.\n
LOCATION:https://researchseminars.org/talk/IMS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Tice (Carnegie Mellon University)
DTSTART:20210513T130000Z
DTEND:20210513T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/80
DESCRIPTION:Title: Tra
veling wave solutions to the free boundary Navier-Stokes equations\nby
Ian Tice (Carnegie Mellon University) as part of PDE seminar via Zoom\n\n
\nAbstract\nConsider a layer of viscous incompressible fluid bounded below
by a flat rigid boundary and above by a moving boundary. The fluid is sub
ject to gravity\, surface tension\, and an external stress that is station
ary when viewed in a coordinate system moving at a constant velocity paral
lel to the lower boundary. The latter can model\, for instance\, a tube bl
owing air on the fluid while translating across the surface. In this talk
we will detail the construction of traveling wave solutions to this proble
m\, which are themselves stationary in the same translating coordinate sys
tem. While such traveling wave solutions to the Euler equations are well-k
nown\, to the best of our knowledge this is the first construction of such
solutions with viscosity. This is joint work with Giovanni Leoni.\n\nhttp
s://nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zaher Hani (University of Michigan)
DTSTART:20210520T130000Z
DTEND:20210520T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/81
DESCRIPTION:Title: Ful
l derivation of the wave kinetic equation\nby Zaher Hani (University o
f Michigan) as part of PDE seminar via Zoom\n\n\nAbstract\nWe will discuss
a recent work\, in collaboration with Yu Deng (USC)\, in which we provide
the rigorous derivation of the wave kinetic equation from the cubic nonli
near Schrödinger (NLS) equation at the kinetic timescale\, under a partic
ular scaling law that describes the limiting process. This solves a main c
onjecture in the theory of wave turbulence\, i.e. the kinetic theory of no
nlinear wave systems. Our result is the wave analog of Lanford's theorem o
n the derivation of the Boltzmann kinetic equation from particle systems\,
where in both cases one takes the thermodynamic limit as the size of the
system diverges to infinity\, and as the interaction strength of waves or
radius of particles vanishes to 0\, according to some specified scaling la
w. This is the first result of its kind for any nonlinear wave system.\n
LOCATION:https://researchseminars.org/talk/IMS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Rosenzweig (MIT)
DTSTART:20211028T130000Z
DTEND:20211028T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/82
DESCRIPTION:Title: Glo
bal solutions of aggregation equations and other flows with random diffusi
on\nby Matthew Rosenzweig (MIT) as part of PDE seminar via Zoom\n\n\nA
bstract\nAggregation equations\, such as the parabolic-elliptic Patlak-Kel
ler-Segel model\, are known to have an optimal threshold for global existe
nce vs. finite-time blow-up. In particular\, if the diffusion is absent\,
then all smooth solutions with finite second moment can exist only locally
in time. Nevertheless\, one can ask whether global existence can be resto
red by adding a suitable noise to the equation\, so that the dynamics are
now stochastic. In this talk\, we investigate whether random diffusion can
restore global existence for a large class of active scalar equations in
arbitrary dimension with possibly singular velocity fields. This class inc
ludes Hamiltonian flows\, such as the SQG equation and its generalizations
\, and gradient flows\, such as those arising in aggregation models. For t
his class\, we show global existence of solutions in Gevrey-type Fourier-L
ebesgue spaces with quantifiable high probability.\n
LOCATION:https://researchseminars.org/talk/IMS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Louis Marzuola (University of North Carolina at Chapel Hill
)
DTSTART:20211104T130000Z
DTEND:20211104T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/83
DESCRIPTION:Title: On
4th order nonlinear thin-film like PDEs describing crystal surface evoluti
on\nby Jeremy Louis Marzuola (University of North Carolina at Chapel H
ill) as part of PDE seminar via Zoom\n\n\nAbstract\nWe discuss recent resu
lts with a number of collaborators on PDEs relating to the relaxation of a
crystal surface. After a brief overview of the motivating microscopic pr
ocess that leads to the models\, we will present results on the well-posed
ness of these models in various settings. Towards the end\, we will show
numerical evidence to motivate a number of open questions about this famil
y of models.\n
LOCATION:https://researchseminars.org/talk/IMS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Spolaor (UC San Diego)
DTSTART:20211111T130000Z
DTEND:20211111T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/84
DESCRIPTION:Title: (Qu
asi-)conformal methods in two-dimensional free boundary problems\nby L
uca Spolaor (UC San Diego) as part of PDE seminar via Zoom\n\n\nAbstract\n
Abstract: In this talk I will explain how to obtain precise informations o
n the structure of the free-boundary to $2$-dimensional solutions of the o
ne and two phase problems at so-called branching points using the theory o
f (quasi-)conformal maps. The talk is based on joint work with G. De Phili
ppis (Courant) and B. Velichkov (Pisa).\n
LOCATION:https://researchseminars.org/talk/IMS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Mingione (University of Parma)
DTSTART:20211118T130000Z
DTEND:20211118T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/85
DESCRIPTION:Title: Per
turbations beyond Schauder\nby Giuseppe Mingione (University of Parma)
as part of PDE seminar via Zoom\n\n\nAbstract\nSo-called Schauder estimat
es are a standard tool in the analysis of linear elliptic and parabolic PD
Es. They had been originally proved by Hopf (1929\, interior case)\, and b
y Schauder and Caccioppoli (1934\, global estimates). Since then\, several
proofs were given (Campanato\, Trudinger\, Simon). The nonlinear case is
a more recent achievement from the 80s (Giaquinta & Giusti\, Ivert\, J. Ma
nfredi\, Lieberman). All these classical results take place in the uniform
ly elliptic case. I will discuss progress in the nonuniformly elliptic one
.\n
LOCATION:https://researchseminars.org/talk/IMS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helena J Nussenzveig Lopes (Universidade Federal do Rio de Janeiro
)
DTSTART:20211202T130000Z
DTEND:20211202T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/86
DESCRIPTION:Title: 2D
Navier-Stokes equations on a bounded domain with holes and Navier friction
boundary conditions\nby Helena J Nussenzveig Lopes (Universidade Fede
ral do Rio de Janeiro) as part of PDE seminar via Zoom\n\n\nAbstract\nWe w
ill discuss the large time behavior of solutions of 2D Navier-Stokes in bo
unded domains which are not necessarily simply connected\, when we impose
Navier friction boundary conditions. We establish exponential time decay\,
for both velocity and vorticity\, under various assumptions on the fricti
on coefficient relative to curvature of the boundary\, for different types
of domains. We also discuss the special role\, played by the disk and the
annulus\, in this analysis. This is joint work with Christophe Lacave\, M
ilton Lopes Filho and Jim Kelliher.\n
LOCATION:https://researchseminars.org/talk/IMS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Binh Tran (Southern Methodist University)
DTSTART:20211216T130000Z
DTEND:20211216T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/87
DESCRIPTION:Title: Som
e Recent Results On Wave Turbulence: Derivation\, Analysis\, Numerics and
Physical Application\nby Minh Binh Tran (Southern Methodist Universit
y) as part of PDE seminar via Zoom\n\n\nAbstract\nWave turbulence describ
es the dynamics of both classical and non-classical nonlinear waves out o
f thermal equilibrium. In this talk\, we will discuss some of our recent
results on some aspects of wave turbulence\, concerning the derivation and
analysis of wave kinetic equations\, some numerical algorithms and physic
al applications in Bose-Einstein Condensates.\n
LOCATION:https://researchseminars.org/talk/IMS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Terracini (Università di Torino)
DTSTART:20220127T130000Z
DTEND:20220127T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/88
DESCRIPTION:Title: Fre
e boundaries in segregation problems\nby Susanna Terracini (Universit
à di Torino) as part of PDE seminar via Zoom\n\nAbstract: TBA\n\nhttps://
nguyenquochung1241.wixsite.com/qhung/post/pde-seminar-via-zoom\n
LOCATION:https://researchseminars.org/talk/IMS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongjie Dong (Brown University)
DTSTART:20220210T130000Z
DTEND:20220210T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/89
DESCRIPTION:Title: Sob
olev estimates for fractional PDEs\nby Hongjie Dong (Brown University)
as part of PDE seminar via Zoom\n\n\nAbstract\nI will discuss some recent
results on Sobolev estimates for fractional elliptic and parabolic equati
ons with or without weights. We considered equations with time fractional
derivatives of the Caputo type\, or with nonlocal derivatives in the space
variables\, or both. This is based on joint work with Doyoon Kim (Korea U
niversity) and Yanze Liu (Brown).\n
LOCATION:https://researchseminars.org/talk/IMS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan-Vasile Matioc (Universität Regensburg)
DTSTART:20220224T130000Z
DTEND:20220224T135000Z
DTSTAMP:20260422T225658Z
UID:IMS/90
DESCRIPTION:Title: The
two-phase quasi-stationary Stokes flow by capillarity in the plane\nb
y Bogdan-Vasile Matioc (Universität Regensburg) as part of PDE seminar vi
a Zoom\n\n\nAbstract\nWe discuss a two-phase moving boundary problem that
describes the two-dimensional quasistationary Stokes flow of two fluids wi
th different densities and viscosities that occupy the entire plane in the
regime where surface tension effects are taken into account at the interf
ace that separates the fluids. In this setting the classical methods of po
tential theory can be used to transform the model into a nonlinear and non
local evolution problem for the function that parameterizes the interface
between the fluids\, the nonlinearities being expressed by singular integr
al operators. This problem is of parabolic type\, well-posed in all Sobole
v spaces up to critical regularity\, and it features some parabolic smooth
ing properties. Joint work with Georg Prokert.\n
LOCATION:https://researchseminars.org/talk/IMS/90/
END:VEVENT
END:VCALENDAR