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BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State University)
DTSTART:20210726T150000Z
DTEND:20210726T155000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/1
DESCRIPTION:Title: Global existence for the 2D Kuramoto-Sivashinsky equation\nby Ann
a Mazzucato (Penn State University) as part of BIRS workshop: New Mechanis
ms for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equation
s\n\n\nAbstract\nI will present recent results concerning global existence
for the Kuramoto-Sivashinsky equation in 2 space dimensions with and with
out advection in the presence of growing modes. The KSE is a model of long
-wave instability in dissipative systems.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hou (California Institute of Technology)
DTSTART:20210726T161000Z
DTEND:20210726T170000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/2
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and nearly
singular solutions of 3D Navier-Stokes equations\nby Tom Hou (Califor
nia Institute of Technology) as part of BIRS workshop: New Mechanisms for
Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\n
Abstract\nWhether the 3D incompressible Euler and Navier-Stokes equations
can develop a finite time singularity from smooth initial data is one of t
he most challenging problems in nonlinear PDEs. In an effort to provide a
rigorous proof of the potential Euler singularity revealed by Luo-Hou's co
mputation\, we develop a novel method of analysis and prove that the origi
nal De Gregorio model and the Hou-Lou model develop a finite time singular
ity from smooth initial data. Using this framework and some techniques fro
m Elgindi's recent work on the Euler singularity\, we prove the finite tim
e blowup of the 2D Boussinesq and 3D Euler equations with $C^{1\,\\alpha}$
initial velocity and boundary. Further\, we present some new numerical ev
idence that the 3D incompressible Euler equations with smooth initial data
develop a potential finite time singularity at the origin\, which is quit
e different from the Luo-Hou scenario. Our study also shows that the 3D N
avier-Stokes equations develop nearly singular solutions with maximum vort
icity increasing by a factor of $10^7$. However\, the viscous effect event
ually dominates vortex stretching and the 3D Navier-Stokes equations narro
wly escape finite-time blowup. Finally\, we present strong numerical evid
ence that the 3D Navier-Stokes equations with slowly decaying viscosity de
velop a finite time singularity.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Nahmod (University of Massachusetts)
DTSTART:20210726T192000Z
DTEND:20210726T201000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/3
DESCRIPTION:Title: Propagation of randomness\, Gibbs measures and random tensors for NLS
\nby Andrea Nahmod (University of Massachusetts) as part of BIRS works
hop: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics
in Fluid Equations\n\n\nAbstract\nWe review recent work\, joint with Yu D
eng and Haitian Yue\, about the Gibbs measure for the periodic 2D NLS and
3D Hartree NLS as well as the theory of random tensors\, a powerful new f
ramework which allows us to unravel the propagation of randomness under th
e nonlinear flow beyond the linear evolution of random data. This enables
us in particular\, to show the existence and uniqueness of solutions to th
e periodic NLS in an optimal range relative to what we define as the proba
bilistic scaling.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (UC Davis)
DTSTART:20210726T203000Z
DTEND:20210726T212000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/4
DESCRIPTION:Title: Simultaneous development of shocks and cusps for 2D compressible Eule
r from smooth initial data\nby Steve Shkoller (UC Davis) as part of BI
RS workshop: New Mechanisms for Regularity\, Singularity\, and Long Time D
ynamics in Fluid Equations\n\n\nAbstract\nA fundamental question in fluid
dynamics concerns the formation of discontinuous shock waves from smooth i
nitial data. We first classify the first singularity\, the so-called $C^
{\\frac{1}{3}} $ pre-shock\, as a fractional series expansion with coeffi
cients computed from the data. With this precise pre-shock description\, w
e prove that a discontinuous shock instantaneously develops after the pre
-shock. This regular shock solution is shown to be unique in a class of
entropy solutions with azimuthal symmetry and regularity determined by the
pre-shock expansion. Simultaneous to the development of the shock front\
, two other characteristic surfaces of cusp-type singularities emerge from
the pre-shock. We prove that along the slowest surface\, all fluid va
riables except the entropy have $C^{1\, {\\frac{1}{2}} }$ one-sided cusps
from the shock side\, and that the normal velocity is decreasing in the di
rection of its motion\; we thus term this surface a weak rarefaction wave
. Along the surface moving with the fluid velocity\, density and entropy
form $C^{1\, {\\frac{1}{2}} }$ one-sided cusps while the pressure and norm
al velocity remain $C^2$\; as such\, we term this surface a weak contact
discontinuity.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Guo (Brown University)
DTSTART:20210727T150000Z
DTEND:20210727T155000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/5
DESCRIPTION:Title: Dynamics of Contact Line\nby Yan Guo (Brown University) as part o
f BIRS workshop: New Mechanisms for Regularity\, Singularity\, and Long Ti
me Dynamics in Fluid Equations\n\n\nAbstract\nContact lines (e.g\, where c
offee meets the coffee cup or a droplet)\nappear generically between a fre
e surface and a fixed boundary. Even\nthough the steady contact line and c
ontact angle was studied by people\nlike Gauss and Young\, even the modell
ing of dynamic contact lines has\nbeen an active research area in physics.
In a joint research program\ninitiated with Ian Tice\, global well-posedn
ess and stability of\ncontact lines is established for a recent viscous fl
uid model in 2D.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (University of California - Los Angeles)
DTSTART:20210727T161000Z
DTEND:20210727T170000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/6
DESCRIPTION:Title: Universality and possible blowup in fluid equations\nby Terence T
ao (University of California - Los Angeles) as part of BIRS workshop: New
Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in Fluid
Equations\n\n\nAbstract\nWe discuss some possible (and still speculative)
routes to establishing finite time blowup in fluid equations (and other PD
E)\, focusing in particular on methods based on establishing universality
properties for such equations.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi (Courant Institute and NYUAD)
DTSTART:20210727T173000Z
DTEND:20210727T182000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/7
DESCRIPTION:by Nader Masmoudi (Courant Institute and NYUAD) as part of BIR
S workshop: New Mechanisms for Regularity\, Singularity\, and Long Time Dy
namics in Fluid Equations\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Deng (University of Southern California)
DTSTART:20210727T192000Z
DTEND:20210727T201000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/8
DESCRIPTION:Title: Full derivation of the wave kinetic equation\nby Yu Deng (Univers
ity of Southern California) as part of BIRS workshop: New Mechanisms for R
egularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nA
bstract\nThe wave kinetic equation is a central topic in the theory of wav
e turbulence\, which concerns the thermodynamic limit of interacting wave
systems. It can be traced back to the 1920s and has played significant rol
es in different areas of physics. However\, the mathematical justification
of the theory has long been open. In this talk we present our recent work
\, which resolves this problem by providing the rigorous derivation of the
wave kinetic equation. This is joint work with Zaher Hani (University of
Michigan).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20210727T203000Z
DTEND:20210727T212000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/9
DESCRIPTION:Title: Gravitational Collapse for Newtonian Stars\nby Juhi Jang (Univers
ity of Southern California) as part of BIRS workshop: New Mechanisms for R
egularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nA
bstract\nA classical model to describe the dynamics of Newtonian stars is
the gravitational Euler-Poisson system. The Euler-Poisson system admits a
wide range of star solutions that are in equilibrium or expand for all tim
e or collapse in a finite time or rotate. In this talk\, I will discuss so
me recent progress on those star solutions with focus on gravitational col
lapse. The talk is based on joint works with Yan Guo and Mahir Hadzic.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Tech)
DTSTART:20210728T150000Z
DTEND:20210728T155000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/10
DESCRIPTION:Title: Small scale formations in the incompressible porous media equation\nby Yao Yao (Georgia Tech) as part of BIRS workshop: New Mechanisms for
Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\
nAbstract\nThe incompressible porous media (IPM) equation describes the ev
olution of density transported by an incompressible velocity field given b
y Darcy’s law. Here the velocity field is related to the density via a s
ingular integral operator\, which is analogous to the 2D SQG equation. The
question of global regularity vs finite-time blow-up remains open for smo
oth initial data\, although numerical evidence suggests that small scale f
ormation can happen as time goes to infinity. In this talk\, I will discus
s rigorous examples of small scale formations in the IPM equation: we cons
truct solutions to IPM that exhibit infinite-in-time growth of Sobolev nor
ms\, provided that they remain globally smooth in time. As an application\
, this allows us to obtain nonlinear\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Constantin (Princeton University)
DTSTART:20210728T161000Z
DTEND:20210728T170000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/11
DESCRIPTION:Title: Nernst-Planck-Navier-Stokes Equations\nby Peter Constantin (Prin
ceton University) as part of BIRS workshop: New Mechanisms for Regularity\
, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbstract\nT
he Nernst-Planck-Navier-Stokes equations model the evolution of ions\nin N
ewtonian fluids. I will describe results on global existence and\nstabilit
y of smmoth solutions and on asymptotic interior electroneutrality\n(the v
anishing of the charge density away from boundaries\, in the limit of zero
Debye\nscreening length). The talk is based on recent works with M. Ignat
ova and with F-N\nLee.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrej Zlatos (University of California San Diego)
DTSTART:20210728T192000Z
DTEND:20210728T201000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/12
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby Andrej Zlatos (Uni
versity of California San Diego) as part of BIRS workshop: New Mechanisms
for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n
\n\nAbstract\nBounded vorticity solutions to the 2D Euler equations on sin
gular domains are typically not close to Lipschitz near boundary singulari
ties\, which makes their uniqueness a difficult open problem. I will pres
ent a general sufficient condition on the geometry of the domain that guar
antees global uniqueness for all solutions initially constant near the bou
ndary. This condition is only slightly more restrictive than exclusion of
corners with angles greater than $\\pi$ and\, in particular\, is satisfie
d by all convex domains. Its proof is based on showing that fluid particl
e trajectories for general bounded vorticity solutions cannot reach the bo
undary in finite time. The condition also turns out to be sharp in the la
tter sense: there are domains that come arbitrarily close to satisfying it
and on which particle trajectories can reach the boundary in finite time.
\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sverak (University of Minnesota)
DTSTART:20210728T203000Z
DTEND:20210728T212000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/13
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby Vladimir Sverak (U
niversity of Minnesota) as part of BIRS workshop: New Mechanisms for Regul
arity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbstr
act\nWe discuss the first few terms in the asymptotic expansion of the sol
utions of $-\\Delta u + u\\nabla u+\\nabla p=f(x)$ at infinity (assuming $
f(x)$ is localized and not too large). The first term has been known for s
ome time and is given by Landau solutions. The higher-order terms exhibit
interesting behavior. \nJoint work with Hao Jia.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Constantin (Vienna University)
DTSTART:20210729T150000Z
DTEND:20210729T155000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/14
DESCRIPTION:Title: Large-amplitude steady downstream water waves\nby Adrian Constan
tin (Vienna University) as part of BIRS workshop: New Mechanisms for Regul
arity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbstr
act\nA study of wave-current interactions in two-dimensional\nwater flows
of constant vorticity over a flat bed is discussed.\nFor large-amplitude p
eriodic traveling waves that propagate at\nthe water surface in the same d
irection as the underlying current\n(downstream waves)\, we prove explicit
uniform bounds for their\namplitude. In particular\, our estimates show t
hat the maximum\namplitude of the waves becomes vanishingly small as the v
orticity\nincreases without limit. We also prove that the downstream waves
\non a global bifurcating branch are never overhanging\, and that their\nm
ass flux and Bernoulli constant are uniformly bounded. This is\njoint work
with Walter Strauss (Brown University\, USA) and Eugen\nVarvaruca (Univer
sity of Iasi\, Romania).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Musso (University of Bath)
DTSTART:20210729T161000Z
DTEND:20210729T170000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/15
DESCRIPTION:Title: Solutions of the incompressible Euler equations with concentrated vo
rticity\nby Monica Musso (University of Bath) as part of BIRS workshop
: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in
Fluid Equations\n\n\nAbstract\nI will discuss solutions to the incompressi
ble Euler equation in two di-mensions with vorticity close to a finite sum
of Dirac deltas (vortices). The law of motion of the vortices was known f
ormally for a long time and proved rigorously by Marchioro-Pulvirenti. In
collaboration with Juan Davila (U.Bath)\, Manuel del Pino(U. Bath)\, and
Juncheng Wei (UBC) we have a different point of view\, which allows a very
precise description of the solution near the vortices. Our construction c
an be generalized to other situations\,such as the construction of leapfro
gging vortex rings of the 3D incompressibleEuler equations.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Seregin (Oxford University)
DTSTART:20210729T173000Z
DTEND:20210729T182000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/16
DESCRIPTION:Title: Local regularity of axisymmetric solutions to Navier-Stokes equation
s\nby Grigory Seregin (Oxford University) as part of BIRS workshop: Ne
w Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in Flui
d Equations\n\n\nAbstract\nThe aim of our talk is to show that axially sym
metric suitable weak solutions to the Navier-Stokes equations have no Type
I blowups. This can be done by reduction to a Liouville type theorem for
a certain governing equation on a scalar function.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tai-Peng Tsai (University of British Columbia)
DTSTART:20210729T192000Z
DTEND:20210729T201000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/17
DESCRIPTION:Title: Local regularity conditions on initial data for local energy solutio
ns of the Navier-Stokes equations\nby Tai-Peng Tsai (University of Bri
tish Columbia) as part of BIRS workshop: New Mechanisms for Regularity\, S
ingularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbstract\nWe s
how local regularity of local energy solutions to the Navier-Stokes equati
ons in terms of local scaled integrals of the initial data. It extends pre
vious work of Jia-Sverak\, Barker-Prange and ourselves. This refined crite
rion implies that if a weighted $L^2$ norm of the initial data is finite\,
then all local energy solutions are regular in a region confined by space
-time hypersurfaces determined by the weight. This result generalizes The
orems C and D of Caffarelli\, Kohn and Nirenberg (Comm. Pure Appl. Math. 3
5\; 1982). This is a joint work with Kyungkeun Kang and Hideyuki Miura.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20210729T203000Z
DTEND:20210729T212000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/18
DESCRIPTION:Title: Long time existence for the Euler-Coriolis system\nby Benoit Pau
sader (Brown University) as part of BIRS workshop: New Mechanisms for Regu
larity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbst
ract\nThis is a joint work with Y. Guo and K. Widmayer. We consider the Eu
ler equation in 3d with a Coriolis force and we show that small\, smooth a
nd localized initial data which are axisymmetric lead to solutions which e
xist for a long time. The proof uses the dispersive effect induced by the
Coriolis term and relies on recent advances for long time estimates for qu
asilinear dispersive equations.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gomez Serrano (Brown University)
DTSTART:20210730T150000Z
DTEND:20210730T155000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/19
DESCRIPTION:Title: Symmetry in stationary and uniformly rotating solutions of fluid equ
ations\nby Javier Gomez Serrano (Brown University) as part of BIRS wor
kshop: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamic
s in Fluid Equations\n\n\nAbstract\nIn this talk\, I will discuss characte
rizations of stationary or uniformly-rotating solutions of 2D Euler and ot
her similar equations. The main question we want to address is whether eve
ry stationary/uniformly-rotating solution must be radially symmetric. Base
d on joint work with Jaemin Park\, Jia Shi and Yao Yao.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20210730T161000Z
DTEND:20210730T170000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/20
DESCRIPTION:by Fabio Pusateri (University of Toronto) as part of BIRS work
shop: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics
in Fluid Equations\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20210730T192000Z
DTEND:20210730T201000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/21
DESCRIPTION:Title: Finite time singularities for some fluid-related equations\nby J
uncheng Wei (University of British Columbia) as part of BIRS workshop: New
Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in Fluid
Equations\n\n\nAbstract\nI will report some recent results on the existen
ce of finite time blow-up for nematic liquid crystal flows and Landau-Lips
chitz-Gilbert equation. The nematic liquid crystal flow is a coupled syst
em of harmonic map flows and Navier-Stokes system while LLG is a standard
model in magnetics. I will show how the gluing techniques can be applied
to both equations to produce blow-ups.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Vasseur (University of Texas at Austin)
DTSTART:20210730T203000Z
DTEND:20210730T212000Z
DTSTAMP:20260422T185714Z
UID:BIRS-21w5110/22
DESCRIPTION:Title: Instability of finite time blow-ups for incompressible Euler\nby
Alexis Vasseur (University of Texas at Austin) as part of BIRS workshop:
New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in Fl
uid Equations\n\n\nAbstract\nIn this talk\, we will discuss the interactio
n between the stability\, and the propagation of regularity\, for solution
s to the incompressible 3D Euler equation. It is still unknown whether a s
olution with smooth initial data can develop a singularity in finite time.
We will describe how\, in such a scenario\, the solution becomes unstable
as time approaches the blow-up time. The method uses the relation between
the vorticity of the solution\, and the bi-characteristic amplitude solut
ions\, which describe the evolution of the linearized Euler equation at hi
gh frequency. In the axisymmetric case\, we can also study the instability
of blow-up profiles. This work was partially supported by the NSF DMS-190
7981. This a joint work with Misha Vishik and Laurent Lafleche.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5110/22/
END:VEVENT
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