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BEGIN:VEVENT
SUMMARY:Joachim Krieger (Ecole Polytechnique Federale de Lausanne)
DTSTART:20210927T150000Z
DTEND:20210927T153500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/1
DESCRIPTION:Title: Recent developments in singularity formation of nonlinear waves\n
by Joachim Krieger (Ecole Polytechnique Federale de Lausanne) as part of B
IRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nI wil
l discuss some recent results and formulate some conjectures on singularit
y formation in the context of geometric wave equations. This comprises joi
nt work with Miao and Schlag and others.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hou (California Institute of Technology)
DTSTART:20210927T162000Z
DTEND:20210927T165500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/2
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and the ne
arly singular behavior of 3D Navier-Stokes equations\nby Tom Hou (Cali
fornia Institute of Technology) as part of BIRS workshop: Singularity Form
ation in Nonlinear PDEs\n\n\nAbstract\nWhether the 3D incompressible Euler
and Navier-Stokes equations can develop a finite time singularity from sm
ooth initial data is one of the most challenging problems in nonlinear PDE
s. In an effort to provide a rigorous proof of the potential Euler singula
rity revealed by Luo-Hou's computation\, we develop a novel method of anal
ysis and prove that the original De Gregorio model and the Hou-Lou model d
evelop a finite time singularity from smooth initial data. Using this fram
ework and some techniques from Elgindi's recent work on the Euler singular
ity\, we prove the finite time blowup of the 2D Boussinesq and 3D Euler eq
uations with $C^{1\,\\alpha}$ initial velocity and boundary. Further\, we
present some new numerical evidence that the 3D incompressible Euler equat
ions with smooth initial data develop a potential finite time singularity
at the origin\, which is quite different from the Luo-Hou scenario. Our s
tudy also shows that the 3D Navier-Stokes equations develop nearly singula
r solutions with maximum vorticity increasing by a factor of $10^7$. Howev
er\, the viscous effect eventually dominates vortex stretching and the 3D
Navier-Stokes equations narrowly escape finite time blowup. Finally\, we
present strong numerical evidence that the 3D Navier-Stokes equations with
slowly decaying time-dependent viscosity develop a finite time singularit
y.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Collot (Cergy Paris Université)
DTSTART:20210927T173000Z
DTEND:20210927T180500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/3
DESCRIPTION:Title: On the derivation of the Kinetic Wave Equation in the inhomogeneous s
etting\nby Charles Collot (Cergy Paris Université) as part of BIRS wo
rkshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe kinetic
wave equation arises in weak wave turbulence theory. In this talk we are
interested in its derivation as an effective equation from dispersive wave
s with quadratic nonlinearity for the microscopic description of a system.
We focus on the space-inhomogeneous case\, which had not been treated ear
lier. More precisely\, we will consider such a dispersive equations in a w
eakly nonlinear regime\, and for highly oscillatory random Gaussian fields
with localised enveloppes as initial data. A conjecture in statistical ph
ysics is that there exists a kinetic time scale on which\, statistically\,
the Wigner transform of the solution (a space dependent local Fourier ene
rgy spectrum) evolve according to the kinetic wave equation. \nI will pres
ent a joint work with Ioakeim Ampatzoglou and Pierre Germain in which we a
pproach the problem of the validity of this kinetic wave equation through
the convergence and stability of the corresponding Dyson series. We are ab
le to identify certain nonlinearities\, dispersion relations\, and regimes
\, and for which the convergence indeed holds almost up to the kinetic tim
e (arbitrarily small polynomial loss).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20210927T181000Z
DTEND:20210927T184500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/4
DESCRIPTION:Title: Internal modes and radiation damping for quadratic KG in 3d\nby F
abio Pusateri (University of Toronto) as part of BIRS workshop: Singularit
y Formation in Nonlinear PDEs\n\n\nAbstract\nWe consider quadratic Klein-G
ordon equations with an external potential $V$ in $3+1$\n space dimensions
. We assume that $V$ is generic and decaying\, and that the operator $H= -
\\Delta+ V+ m^2$ has an eigenvalue $\\lambda^2 < m^2$. This is a so-calle
d ‘internal mode’ and gives rise to\n time-periodic localized solution
s of the linear flow. We address the question of whether such\n solutions
persist under the full nonlinear flow. Our main result shows that all smal
l nonlinear\n solutions slowly decay as the energy is transferred from the
internal mode to the continuous\n spectrum\, provided a natural Fermi gol
den rule holds. This extends the seminal work of\n Soffer-Weinstein for cu
bic nonlinearities to the case of any generic perturbation. This is joint\
n work with T. L\\'eger (Princeton University).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilhelm Schlag (Yale University)
DTSTART:20210927T185000Z
DTEND:20210927T192500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/6
DESCRIPTION:Title: Asymptotic stability for the Sine-Gordon kink under odd perturbations
\nby Wilhelm Schlag (Yale University) as part of BIRS workshop: Singul
arity Formation in Nonlinear PDEs\n\n\nAbstract\nWe will describe the rece
nt asymptotic analysis with Jonas Luehrmann of the Sine-Gordon evolution o
f odd data near the kink. We do not rely on the complete integrability of
the problem in a direct way\, in particular we do not use the inverse scat
tering transform.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel del Pino (University of Bath)
DTSTART:20210927T154000Z
DTEND:20210927T161500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/7
DESCRIPTION:Title: Dynamics of concentrated vorticities in 2d and 3d Euler flows\nby
Manuel del Pino (University of Bath) as part of BIRS workshop: Singularit
y Formation in Nonlinear PDEs\n\n\nAbstract\nA classical problem that trac
es back to Helmholtz and Kirchhoff is the understanding of the dynamics of
solutions to the Euler equations of an inviscid incompressible fluid\, wh
en the vorticity of the solution is initially concentrated near isolated p
oints in 2d or vortex lines in 3d. We discuss some recent results on the e
xistence and asymptotic behaviour of these solutions. We describe\, with p
recise asymptotics\, interacting vortices\, and travelling helices. We rig
orously establish the law of motion of ”leapfrogging vortex rings”\, o
riginally conjectured by Helmholtz in 1858. This is joint work with Juan D
avila\, Monica Musso\, and Juncheng Wei.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Yu (The Chinese University of Hong Kong)
DTSTART:20210928T150000Z
DTEND:20210928T153500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/8
DESCRIPTION:Title: Patterns in spherical droplets\nby Yong Yu (The Chinese Universit
y of Hong Kong) as part of BIRS workshop: Singularity Formation in Nonline
ar PDEs\n\n\nAbstract\nIn this talk\, I will introduce the spherical dropl
et problem in the Landau-de Gennes\n theory. With a novel bifurcation diag
ram\, we find solutions with ring and split-core disclinations.\n This wor
k theoretically confirms the numerical results of Gartland and Mkaddem in
2000.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20210928T154000Z
DTEND:20210928T161500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/9
DESCRIPTION:Title: Boundary layer models of the Hou-Luo scenario\nby Alexander Kisel
ev (Duke University) as part of BIRS workshop: Singularity Formation in No
nlinear PDEs\n\n\nAbstract\nThe question of singularity formation vs globa
l regularity for the 3D\n Euler equation is a major open problem.\n Seve
ral years ago\, Hou and Luo proposed a new scenario for singularity\n for
mation based on extensive numerical simulations.\n Several 1D models of t
he scenario have been analyzed rigorously and they\n all lead to finite t
ime blow up for some\n initial data. In this work\, we explore a 2D model
that aims to gain\n insight into the mechanics of boundary layer\n wher
e extreme growth of vorticity is observed. We isolate a\n regularization
mechanism and build a simplified model\n around it which is globally regu
lar. For a more realistic model\, we\n prove finite time blow up.\n This
is a joint work with Siming He (Duke University).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Jia (University of Minnesota)
DTSTART:20210928T162000Z
DTEND:20210928T165500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/10
DESCRIPTION:Title: Some recent progress on asymptotic stability for shear flows and vor
tices\nby Hao Jia (University of Minnesota) as part of BIRS workshop:
Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nIn the talk\, we wi
ll review some recent work on nonlinear asymptotic stability of the two di
mensional incompressible Euler equations\, with a focus on shear flows and
vortices. Some open problems will also be discussed.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiahong Wu (Oklahoma State University)
DTSTART:20210928T173000Z
DTEND:20210928T180500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/11
DESCRIPTION:Title: Stabilization and prevention of potential singularity formation\
nby Jiahong Wu (Oklahoma State University) as part of BIRS workshop: Singu
larity Formation in Nonlinear PDEs\n\n\nAbstract\nThis talk presents two e
xamples of the smoothing and stabilizing phenomenon for coupled PDE\n syst
ems that prevents potential finite-time singularity formation. The 3D inco
mpressible Euler equation\n can potentially develop finite-time singularit
ies\, as indicated by recent numerical simulations and\n theoretical resul
ts. However\, when the Euler equation is coupled with the equation of the
non-Newtonian\n stress tensor via the Oldroyd-B model\, small data global
well-posedness can be established and the\n coupling prevents the potentia
l singularity. A 2D incompressible Euler-like equation with an extra Riesz
\n transform term is not known to be globally well-posed. But\, when coupl
ed with the magnetic field via the\n magneto-hydrodynamic (MHD) system\, w
e can show the global well-posedness near a background magnetic\n field wi
th explicit decay rates. The magnetic field stabilizes the fluid.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi
DTSTART:20210928T181000Z
DTEND:20210928T184500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/12
DESCRIPTION:by Nader Masmoudi as part of BIRS workshop: Singularity Format
ion in Nonlinear PDEs\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tai-Peng Tsai (University of British Columbia)
DTSTART:20210928T185000Z
DTEND:20210928T192500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/13
DESCRIPTION:Title: Finite energy Navier-Stokes flows with unbounded gradients induced b
y localized flux in the half-space\nby Tai-Peng Tsai (University of Br
itish Columbia) as part of BIRS workshop: Singularity Formation in Nonline
ar PDEs\n\n\nAbstract\nFor the Stokes system in the half space\, Kang [Mat
h.Ann.2005] showed that a solution generated by a compactly supported\, H\
\"older continuous boundary flux may have unbounded normal derivatives nea
r the boundary. We first prove explicit global pointwise estimates of a sl
ightly revised solution\, showing in particular that it has finite global
energy and its derivatives blow up everywhere on the boundary away from th
e flux. We then use the above solution as a profile to construct solutions
of the Navier-Stokes equations which also have finite global energy and u
nbounded normal derivatives due to the flux. Our main tool is the pointwis
e estimates of the Green tensor of the Stokes system proved by us in an ea
rlier paper.\n We also examine the Stokes flows generated by dipole bumps
boundary flux\, and identify the regions where the normal derivatives of t
he solutions tend to positive or negative infinity near the boundary. This
is a joint work with Kyungkeun Kang\, Baishun Lai and Chen-Chih Lai.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Roman (Catholic University of Chile)
DTSTART:20210928T193000Z
DTEND:20210928T200500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/14
DESCRIPTION:Title: Vortex lines in the 3D Ginzburg-Landau model of superconductivity\nby Carlos Roman (Catholic University of Chile) as part of BIRS workshop
: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe Ginzburg-Land
au model is a phenomenological description of superconductivity. A crucial
feature is the occurrence of vortex lines\, which appear above a certain
value of the strength of the applied magnetic field called the first criti
cal field. In this talk I will present a sharp estimate of this value and
report on a joint work with Etienne Sandier and Sylvia Serfaty in which we
study the onset of vortex lines and derive an interaction energy for them
.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Zhan (Chinese Academy of Science)
DTSTART:20210929T150000Z
DTEND:20210929T153500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/15
DESCRIPTION:Title: On global hydrostatic approximation of hyperbolic Navier-Stokes syst
em with small Gevrey class 2 data\nby Ping Zhan (Chinese Academy of Sc
ience) as part of BIRS workshop: Singularity Formation in Nonlinear PDEs\n
\n\nAbstract\nWe study a hyperbolic version of the Navier-Stokes equation
s obtained by using Cattaneo heat transfer law instead of Fourier law\, e
volving in a thin strip $\\RR\\times (0\,\\varepsilon)$. The formal limit
of these equations is a hyperbolic Prandtl type equation. We prove the e
xistence and uniqueness of a global solution to these equations under a un
iform smallness assumption on the data in Gevrey 2 class. Then we justify
the limit from the anisotropic hyperbolic Navier-Stokes system to the hydr
ostatic hyperbolic Navier-Stokes system with Gevrey 2 data. We also exhibi
t smallness assumptions on the data in Gevrey 2 class\, under which the so
lutions are global in time.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changyou Wang (Purdue University)
DTSTART:20210929T154000Z
DTEND:20210929T161500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/16
DESCRIPTION:Title: Partial regularity of a nematic liquid crystal flow with kinematic t
ransport effects\nby Changyou Wang (Purdue University) as part of BIRS
workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nMotivate
d by the non-corotational Beris-Edwards $Q$-tensor system modeling the hyd
rodynamic of nematic liquid crystal materials\, we consider the correspond
ing Ericksen vectorial model that\n Includes kinematic transport paramete
rs for molecules of various shapes and show that there exists a global wea
k solution in dimension three\, which is smooth away from a closed set wit
h Hausdorff dimension at most $15/7$.\n This is a joint work with Hengrong
Du.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Pistoia (Sapienza Università di Roma)
DTSTART:20210929T162000Z
DTEND:20210929T165500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/17
DESCRIPTION:Title: Critical Lane-Emden systems\nby Angela Pistoia (Sapienza Univers
ità di Roma) as part of BIRS workshop: Singularity Formation in Nonlinear
PDEs\n\n\nAbstract\nI will present some recent results concerning non-deg
eneracy\, existence and multiplicity of solutions to a Lane-Emden critical
system\n obtained in collaboration with R.Frank and S.Kim.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otis Chodosh (Stanford University)
DTSTART:20210929T173000Z
DTEND:20210929T180500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/18
DESCRIPTION:Title: The p-widths of a surface\nby Otis Chodosh (Stanford University)
as part of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAb
stract\nThe p-widths of a Riemannian manifold were introduced by Gromov as
a nonlinear version of the eigenvalues of the Laplacian (replacing the Di
richlet energy on functions with the area functional on submanifolds). I w
ill discuss recent work with C. Mantoulidis (Rice) concerning the p-widths
on surfaces\, using in particular Liu—Wei’s analysis of entire soluti
ons to the sine-Gordon equation on the plane. In particular\, we prove tha
t the p-widths on a surface correspond to immersed geodesics (instead of g
eodesic nets) and we compute the entire p-width spectrum of $ S^2$ yieldin
g the constant in the Liokumovich—Marques—Neves Weyl law in this dimen
sion.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Souplet (Université Sorbonne Paris Nord)
DTSTART:20210929T181000Z
DTEND:20210929T184500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/19
DESCRIPTION:Title: Some recent Liouville type results and their applications\nby Ph
ilippe Souplet (Université Sorbonne Paris Nord) as part of BIRS workshop:
Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe p-widths of a
Riemannian manifold were introduced by Gromov as a nonlinear version of th
e eigenvalues of the Laplacian (replacing the Dirichlet energy on function
s with the area functional on submanifolds). I will discuss recent work wi
th C. Mantoulidis (Rice) concerning the p-widths on surfaces\, using in pa
rticular Liu—Wei’s analysis of entire solutions to the sine-Gordon equ
ation on the plane. In particular\, we prove that the p-widths on a surfac
e correspond to immersed geodesics (instead of geodesic nets) and we compu
te the entire p-width spectrum of $ S^2$ yielding the constant in the Liok
umovich—Marques—Neves Weyl law in this dimension.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christos Mantoulidis (Rice University)
DTSTART:20210929T185000Z
DTEND:20210929T192500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/20
DESCRIPTION:Title: Mean curvature flow with generic initial data\nby Christos Manto
ulidis (Rice University) as part of BIRS workshop: Singularity Formation i
n Nonlinear PDEs\n\n\nAbstract\nWe discuss why the mean curvature flow of
generic closed surfaces in ${\\mathbb R}^3$ avoids asymptotically conical
and non-spherical compact singularities. We also discuss why the mean curv
ature flow of generic closed low-entropy hypersurfaces in ${\\mathbb R}^4$
is smooth until it disappears in a round point. This is joint work with O
. Chodosh\, K. Choi\, and F. Schulze.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Tonegawa (Tokyo Institute of Technology)
DTSTART:20210929T193000Z
DTEND:20210929T200500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/21
DESCRIPTION:Title: Existence of canonical multi-phase mean curvature flows\nby Yosh
ihiro Tonegawa (Tokyo Institute of Technology) as part of BIRS workshop: S
ingularity Formation in Nonlinear PDEs\n\n\nAbstract\nI present a recent e
xistence result for multi-phase Brakke flow starting\n from arbitrary part
ition with locally finite co-dimension 1 Hausdorff measure\n which improve
s on my own work with Lami Kim in 2017. The new aspect is that\n the flow
has a character of BV solution\, a notion introduced by \n Luckhaus-Sturze
nhecker in 1995\, in addition to being a Brakke flow.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John King (Tokyo Institute of Technology)
DTSTART:20210930T150000Z
DTEND:20210930T153500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/22
DESCRIPTION:Title: Some blow-up and post-blow-up results for quasilinear reaction diffu
sion\nby John King (Tokyo Institute of Technology) as part of BIRS wor
kshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nSome formal
asymptotic results will be presented.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marek Fila (Comenius University)
DTSTART:20210930T154000Z
DTEND:20210930T161500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/23
DESCRIPTION:Title: Solutions with snaking singularities for the fast diffusion equation
\nby Marek Fila (Comenius University) as part of BIRS workshop: Singul
arity Formation in Nonlinear PDEs\n\n\nAbstract\nWe construct solutions of
the fast diffusion equation\, which exist for\nall $t\\in {\\mathbb R}$ a
nd are singular on the set $\\Gamma(t):= \\{ \\xi(s) \;\ns \\leq ct \\}$\
, $c>0$\, where $\\xi \\in C^3({\\mathbb R}\;{\\mathbb R}^n)$ \, $n\\geq 2
$.\n We also give a precise description of the behavior of the solutions
near\n $\\Gamma(t)$. This is a joint work with John King\, Jin Takahashi
and Eiji\n Yanagida.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Seis (Munster University)
DTSTART:20210930T162000Z
DTEND:20210930T165500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/24
DESCRIPTION:Title: Leading order asymptotics for fast diffusion on bounded domains\
nby Christian Seis (Munster University) as part of BIRS workshop: Singular
ity Formation in Nonlinear PDEs\n\n\nAbstract\nOn a smooth bounded Euclide
an domain\, Sobolev-subcritical fast diffusion with vanishing boundary tr
ace leads to finite-time extinction\, with a vanishing profile selected by
the initial datum. In rescaled variables\, we quantify the rate of conver
gence to this profile uniformly in relative error\, showing the rate is e
ither exponentially fast (with a rate constant predicted by the spectral g
ap) or algebraically slow (which is only possible in the presence of zero
modes). In the first case\, we identify the leading order asymptotics. Our
results improve various results in the literature\, while shortening the
ir proofs. Joint work with Beomjun Choi and Robert J. McCann.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Contreras (New Mexico State Univerity)
DTSTART:20210930T173000Z
DTEND:20210930T180500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/25
DESCRIPTION:Title: Stable vortex configurations with unbounded vorticity in Ginzburg-La
ndau theory\nby Andres Contreras (New Mexico State Univerity) as part
of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nI
n Ginzburg-Landau theory\, the presence of a strong magnetic field allows
for the existence of stable vortex states. The study of global minimizers
of the Ginzburg-Landau energy in $2d$ and a characterization of their vort
icities is the focus of a series of works by Sandier and Serfaty in the$\\
varepsilon \\to 0$ limit\, where $\\varepsilon$is the inverse of the Ginzb
urg-Landau parameter. However\, the full range of existence of stable conf
igurations with prescribed vorticity\, different from the optimal one\, re
mains an open problem. In particular\, it is expected that local minimizer
s with $1\\ll N\\sim 1/\\varepsilon^\\alpha\,$ for some $\\alpha>0$ should
exist\, provided the magnetic field is strong enough. The best partial re
sults until recently could only cover very slowly diverging ($N\\lesssim |
\\log \\varepsilon|$)numbers of vortices. In joint work with R. L. Jerrard
\, we prove the existence of local minimizers with prescribed vorticity fo
r a wide range of external fields and treat for the first timea number ofv
ortices comparable to a power of $1/\\varepsilon.$\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins University)
DTSTART:20210930T181000Z
DTEND:20210930T184500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/26
DESCRIPTION:Title: A new Ginzburg-Landau approximation for the heat flow of harmonic ma
ps with free boundary and partial regularity of weak solutions\nby Yan
nick Sire (Johns Hopkins University) as part of BIRS workshop: Singularity
Formation in Nonlinear PDEs\n\n\nAbstract\nHarmonic maps with free bounda
ry are rather old objects in geometry which has been used recently in seve
ral results related to the co-dimension one conjecture\, extremal metrics
of Steklov eigenvalues or liquid crystal flows. I will report on recent re
sults on a new approximation of these maps which allows to better capture
the boundary behavior and construct weak solutions of the associated heat
flow. I will also give a small energy criterion which allows to prove part
ial regularity of the solutions.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose' Antonio Carrillo (University of Oxford)
DTSTART:20210930T185000Z
DTEND:20210930T192500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/27
DESCRIPTION:Title: Nonlocal Aggregation-Diffusion Equations: entropies\, gradient flows
\, phase transitions and application\nby Jose' Antonio Carrillo (Unive
rsity of Oxford) as part of BIRS workshop: Singularity Formation in Nonlin
ear PDEs\n\n\nAbstract\nThis talk will be devoted to an overview of recent
results understanding the bifurcation analysis of nonlinear Fokker-Planck
equations arising in a myriad of applications such as consensus formation
\, optimization\, granular media\, swarming behavior\, opinion dynamics an
d financial mathematics to name a few. We will present several results rel
ated to localized Cucker-Smale orientation dynamics\, McKean-Vlasov equati
ons\, and nonlinear diffusion Keller-Segel type models in several settings
. We will show the existence of continuous or discontinuous phase transiti
ons on the torus under suitable assumptions on the Fourier modes of the in
teraction potential. The analysis is based on linear stability in the righ
t functional space associated to the regularity of the problem at hand. Wh
ile in the case of linear diffusion\, one can work in the L2 framework\, n
onlinear diffusion needs the stronger Linfty topology to proceed with the
analysis based on Crandall-Rabinowitz bifurcation analysis applied to the
variation of the entropy functional. Explicit examples show that the globa
l bifurcation branches can be very complicated. Stability of the solutions
will be discussed based on numerical simulations with fully explicit ener
gy decaying finite volume schemes specifically tailored to the gradient fl
ow structure of these problems. The theoretical analysis of the asymptotic
stability of the different branches of solutions is a challenging open pr
oblem. This overview talk is based on several works in collaboration with
R. Bailo\, A. Barbaro\, J. A. Canizo\, X. Chen\, P. Degond\, R. Gvalani\,
J. Hu\, G. Pavliotis\, A. Schlichting\, Q. Wang\, Z. Wang\, and L. Zhang.
This research has been funded by EPSRC EP/P031587/1 and ERC Advanced Grant
Nonlocal-CPD 883363.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liqun Zhang (Chinese Academy of Sciences)
DTSTART:20211001T142000Z
DTEND:20211001T145500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/28
DESCRIPTION:Title: The blow up solutions to Boussinesq equations on R3 with dispersive
temperature\nby Liqun Zhang (Chinese Academy of Sciences) as part of B
IRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe t
hree-dimensional incompressible Boussinesq system is one of the important
equations in fluid dynamics. The system describes the motion of temperatur
e-dependent incompressible flows. And the temperature naturally has diffus
ion. Very recently\, Elgindi\, Ghoul and Masmoudi constructed a $C^{1\,\\a
lpha}$ finite time blow-up solutions for Euler systems with finite energy.
Inspired by their works\, we constructed $C^{1\,\\alpha}$ finite time blo
w-up solution for Boussinesq equations where temperature has diffusion and
finite energy. The main difficulty is that the Laplace operator of temper
ature equation is not coercive under Sobolev weighted norm which is introd
uced by Elgindi. We introduced a new time scaling formulation and new weig
hted Sobolev norms\, under which we obtain the coercivity estimate. The ne
w norm is well-coupled with the original norm\, which enable us to finish
the proof.\n This is a jointed work with Gao Chen and Zhang Xianliang.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Davila (Universiy of Bath)
DTSTART:20211001T150000Z
DTEND:20211001T153500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/29
DESCRIPTION:Title: Blow-up for the Keller-Segel system in the critical mass case\nb
y Juan Davila (Universiy of Bath) as part of BIRS workshop: Singularity Fo
rmation in Nonlinear PDEs\n\n\nAbstract\nWe consider the Keller-Segel syst
em in the plane with an initial\n condition with suitable decay and critic
al mass 8 pi.\n We find a function $u_0$ with mass $8 \\pi$ such that\n fo
r any initial condition sufficiently close to $u_0$ and mass $8 \\pi$\,\n
the solution is globally defined and blows up in infinite time. We also fi
nd the\n profile and rate of blow-up. This result answers affirmatively th
e\n question of the nonradial stability raised by Ghoul and Masmoudi\n (20
18). This is joint work with Manuel del Pino (U. of Bath)\, Jean Dolbeault
(U. Paris Dauphine)\, Monica Musso (U. of Bath) and Juncheng Wei (UBC)\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panagiota Daskalopoulos (Columbia University)
DTSTART:20211001T154000Z
DTEND:20211001T161500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/30
DESCRIPTION:Title: Type II smoothing in Mean curvature flow\nby Panagiota Daskalopo
ulos (Columbia University) as part of BIRS workshop: Singularity Formation
in Nonlinear PDEs\n\n\nAbstract\nIn 1994 Velázquez constructed a smooth
\\( O(4)\\times O(4)\\) invariant\n Mean Curvature Flow that forms a typ
e-II singularity at the origin in\n space-time. Stolarski very recently
showed that the mean curvature\n on this solution is uniformly bounded.
Earlier\, Velázquez also provided\n formal asymptotic expansions for a
possible smooth continuation of the\n solution after the singularity. \n
Jointly with S. Angenent and N. Sesum we establish the short time exist
ence of Velázquez' formal \n continuation\, and we verify that the mean
curvature is also uniformly bounded on the continuation.\n Combined with
the earlier results of Velázquez--Stolarski we therefore show\n that th
ere exists a solution \\(\\{M_t^7\\subset\\RR^8 \\mid -t_0 Two non-conventional inequalities\nby Jean Dolbeault (Universit
é Paris-Dauphine) as part of BIRS workshop: Singularity Formation in Nonl
inear PDEs\n\n\nAbstract\nThis lecture is devoted to two inequalities:\n (
1) Reverse Hardy-Littlewood-Sobolev inequalities\,\n (2) Two-dimensional l
ogarithmic inequalities.\n None of these inequalities is classical. Both r
aise interesting open questions\,\n with applications to nonlinear diffusi
ons and Schroödinger equations\n This corresponds to joint results obtain
ed with: (1) Jose A. Carrillo\, Matias G. Delgadino\, Rupert L. Frank\, Fr
anca Hoffmann (2) Rupert L. Frank\, Louis Jeanjean.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slim Ibrahim (University of Victoria)
DTSTART:20211001T173000Z
DTEND:20211001T180500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/32
DESCRIPTION:Title: Revisit singularity formation for the inviscid primitive equation\nby Slim Ibrahim (University of Victoria) as part of BIRS workshop: Sing
ularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe primitive equation
is an important model for large scale fluid model including oceans and atm
osphere. While solutions to the viscous model enjoy global regularity\, in
viscid solutions may develop singularities in finite time. In this talk\,
I will review the methods to show blowup\, and case share more recent prog
ress on qualitative properties of singularity formation.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (Kelei Wang) (University of British Columbia)
DTSTART:20211001T181000Z
DTEND:20211001T184500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/33
DESCRIPTION:Title: Nonexistence of Type II blowups for an energy critical nonlinear hea
t equation\nby Juncheng Wei (Kelei Wang) (University of British Columb
ia) as part of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\
nAbstract\nWe consider the energy critical heat equation \n $$ u_t=\\Delta
u+ u^{\\frac{n+2}{n-2}}\, u(x\,0)= u_0 $$\n We prove that if $n\\geq 7$ a
nd $ u_0\\geq 0$\, then any blow-up must be of Type I. (In the radially s
ymmetric case\, $n\\geq 5$). The proof uses some ideas from geometric mea
sure theory and a reverse inner-outer gluing mechanism.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanghua Lin (New York University)
DTSTART:20211001T185000Z
DTEND:20211001T192500Z
DTSTAMP:20260422T185859Z
UID:BIRS-21w5503/34
DESCRIPTION:Title: Relaxed Energies\, Defect measures and Minimal Currents ↓\nby
Fanghua Lin (New York University) as part of BIRS workshop: Singularity Fo
rmation in Nonlinear PDEs\n\n\nAbstract\nAfter a brief discussion for harm
onic map problems from a three-ball into the two-sphere\, we review on an
open problem posed by R.Schoen\, the notions of relaxed energy\, minimal c
onnection and some results in the late 1980s by several groups. We then f
ocus on a higher dimensional version of these studies. And we shall prese
nt a solution to an open problem proposed by Brezis-Mironescu recently.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5503/34/
END:VEVENT
END:VCALENDAR