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BEGIN:VEVENT
SUMMARY:Joachim Krieger (Ecole Polytechnique Federale de Lausanne)
DTSTART:20210927T150000Z
DTEND:20210927T153500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/1
DESCRIPTION:Title: Recent developments in singularity formation of nonlinear wave
s\nby Joachim Krieger (Ecole Polytechnique Federale de Lausanne) as pa
rt of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract
\nI will discuss some recent results and formulate some conjectures on sin
gularity formation in the context of geometric wave equations. This compri
ses joint work with Miao and Schlag and others.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hou (California Institute of Technology)
DTSTART:20210927T162000Z
DTEND:20210927T165500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/2
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and
the nearly singular behavior of 3D Navier-Stokes equations\nby Tom Ho
u (California Institute of Technology) as part of BIRS workshop: Singulari
ty Formation in Nonlinear PDEs\n\n\nAbstract\nWhether the 3D incompressibl
e Euler and Navier-Stokes equations can develop a finite time singularity
from smooth initial data is one of the most challenging problems in nonlin
ear PDEs. In an effort to provide a rigorous proof of the potential Euler
singularity revealed by Luo-Hou's computation\, we develop a novel method
of analysis and prove that the original De Gregorio model and the Hou-Lou
model develop a finite time singularity from smooth initial data. Using th
is framework and some techniques from Elgindi's recent work on the Euler s
ingularity\, we prove the finite time blowup of the 2D Boussinesq and 3D E
uler equations with $C^{1\,\\alpha}$ initial velocity and boundary. Furthe
r\, we present some new numerical evidence that the 3D incompressible Eule
r equations with smooth initial data develop a potential finite time singu
larity at the origin\, which is quite different from the Luo-Hou scenario.
Our study also shows that the 3D Navier-Stokes equations develop nearly
singular solutions with maximum vorticity increasing by a factor of $10^7$
. However\, the viscous effect eventually dominates vortex stretching and
the 3D Navier-Stokes equations narrowly escape finite time blowup. Finall
y\, we present strong numerical evidence that the 3D Navier-Stokes equatio
ns with slowly decaying time-dependent viscosity develop a finite time sin
gularity.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Collot (Cergy Paris Université)
DTSTART:20210927T173000Z
DTEND:20210927T180500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/3
DESCRIPTION:Title: On the derivation of the Kinetic Wave Equation in the inhomoge
neous setting\nby Charles Collot (Cergy Paris Université) as part of
BIRS workshop: 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 dispersi
ve waves with quadratic nonlinearity for the microscopic description of a
system. We focus on the space-inhomogeneous case\, which had not been trea
ted earlier. More precisely\, we will consider such a dispersive equations
in a weakly nonlinear regime\, and for highly oscillatory random Gaussian
fields with localised enveloppes as initial data. A conjecture in statist
ical physics is that there exists a kinetic time scale on which\, statisti
cally\, the Wigner transform of the solution (a space dependent local Four
ier energy spectrum) evolve according to the kinetic wave equation. \nI wi
ll present a joint work with Ioakeim Ampatzoglou and Pierre Germain in whi
ch we approach the problem of the validity of this kinetic wave equation t
hrough the convergence and stability of the corresponding Dyson series. We
are able to identify certain nonlinearities\, dispersion relations\, and
regimes\, and for which the convergence indeed holds almost up to the kine
tic time (arbitrarily small polynomial loss).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20210927T181000Z
DTEND:20210927T184500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/4
DESCRIPTION:Title: Internal modes and radiation damping for quadratic KG in 3d\nby Fabio Pusateri (University of Toronto) as part of BIRS workshop: Sin
gularity Formation in Nonlinear PDEs\n\n\nAbstract\nWe consider quadratic
Klein-Gordon equations with an external potential $V$ in $3+1$\n space dim
ensions. We assume that $V$ is generic and decaying\, and that the operato
r $H= - \\Delta+ V+ m^2$ has an eigenvalue $\\lambda^2 < m^2$. This is a s
o-called ‘internal mode’ and gives rise to\n time-periodic localized s
olutions of the linear flow. We address the question of whether such\n sol
utions persist under the full nonlinear flow. Our main result shows that a
ll small nonlinear\n solutions slowly decay as the energy is transferred f
rom the internal mode to the continuous\n spectrum\, provided a natural Fe
rmi golden rule holds. This extends the seminal work of\n Soffer-Weinstein
for cubic nonlinearities to the case of any generic perturbation. This is
joint\n work with T. L\\'eger (Princeton University).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilhelm Schlag (Yale University)
DTSTART:20210927T185000Z
DTEND:20210927T192500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/6
DESCRIPTION:Title: Asymptotic stability for the Sine-Gordon kink under odd pertur
bations\nby Wilhelm Schlag (Yale University) as part of BIRS workshop:
Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nWe will describe t
he recent asymptotic analysis with Jonas Luehrmann of the Sine-Gordon evol
ution of odd data near the kink. We do not rely on the complete integrabil
ity of the problem in a direct way\, in particular we do not use the inver
se scattering transform.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel del Pino (University of Bath)
DTSTART:20210927T154000Z
DTEND:20210927T161500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/7
DESCRIPTION:Title: Dynamics of concentrated vorticities in 2d and 3d Euler flows<
/a>\nby Manuel del Pino (University of Bath) as part of BIRS workshop: Sin
gularity Formation in Nonlinear PDEs\n\n\nAbstract\nA classical problem th
at traces back to Helmholtz and Kirchhoff is the understanding of the dyna
mics of solutions to the Euler equations of an inviscid incompressible flu
id\, when the vorticity of the solution is initially concentrated near iso
lated points in 2d or vortex lines in 3d. We discuss some recent results o
n the existence and asymptotic behaviour of these solutions. We describe\,
with precise asymptotics\, interacting vortices\, and travelling helices.
We rigorously establish the law of motion of ”leapfrogging vortex rings
”\, originally conjectured by Helmholtz in 1858. This is joint work with
Juan Davila\, Monica Musso\, and Juncheng Wei.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong Yu (The Chinese University of Hong Kong)
DTSTART:20210928T150000Z
DTEND:20210928T153500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/8
DESCRIPTION:Title: Patterns in spherical droplets\nby Yong Yu (The Chinese Un
iversity of Hong Kong) as part of BIRS workshop: Singularity Formation in
Nonlinear PDEs\n\n\nAbstract\nIn this talk\, I will introduce the spherica
l droplet problem in the Landau-de Gennes\n theory. With a novel bifurcati
on diagram\, we find solutions with ring and split-core disclinations.\n T
his work theoretically confirms the numerical results of Gartland and Mkad
dem in 2000.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20210928T154000Z
DTEND:20210928T161500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/9
DESCRIPTION:Title: Boundary layer models of the Hou-Luo scenario\nby Alexande
r Kiselev (Duke University) as part of BIRS workshop: Singularity Formatio
n in Nonlinear PDEs\n\n\nAbstract\nThe question of singularity formation v
s global regularity for the 3D\n Euler equation is a major open problem.\
n Several years ago\, Hou and Luo proposed a new scenario for singularity
\n formation based on extensive numerical simulations.\n Several 1D mode
ls of the scenario have been analyzed rigorously and they\n all lead to f
inite time blow up for some\n initial data. In this work\, we explore a 2
D model that aims to gain\n insight into the mechanics of boundary layer\
n where extreme growth of vorticity is observed. We isolate a\n regulari
zation mechanism and build a simplified model\n around it which is global
ly regular. 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://stable.researchseminars.org/talk/BIRS-21w5503/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hao Jia (University of Minnesota)
DTSTART:20210928T162000Z
DTEND:20210928T165500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/10
DESCRIPTION:Title: Some recent progress on asymptotic stability for shear flows
and vortices\nby Hao Jia (University of Minnesota) as part of BIRS wor
kshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nIn the talk\
, we will review some recent work on nonlinear asymptotic stability of the
two dimensional incompressible Euler equations\, with a focus on shear fl
ows and vortices. Some open problems will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiahong Wu (Oklahoma State University)
DTSTART:20210928T173000Z
DTEND:20210928T180500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/11
DESCRIPTION:Title: Stabilization and prevention of potential singularity formati
on\nby Jiahong Wu (Oklahoma State University) as part of BIRS workshop
: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThis talk present
s two examples of the smoothing and stabilizing phenomenon for coupled PDE
\n systems that prevents potential finite-time singularity formation. The
3D incompressible Euler equation\n can potentially develop finite-time sin
gularities\, as indicated by recent numerical simulations and\n theoretica
l results. 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 p
otential singularity. A 2D incompressible Euler-like equation with an extr
a Riesz\n transform term is not known to be globally well-posed. But\, whe
n coupled with the magnetic field via the\n magneto-hydrodynamic (MHD) sys
tem\, we can show the global well-posedness near a background magnetic\n f
ield with explicit decay rates. The magnetic field stabilizes the fluid.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi
DTSTART:20210928T181000Z
DTEND:20210928T184500Z
DTSTAMP:20260404T042246Z
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://stable.researchseminars.org/talk/BIRS-21w5503/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tai-Peng Tsai (University of British Columbia)
DTSTART:20210928T185000Z
DTEND:20210928T192500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/13
DESCRIPTION:Title: Finite energy Navier-Stokes flows with unbounded gradients in
duced by localized flux in the half-space\nby Tai-Peng Tsai (Universit
y of British Columbia) as part of BIRS workshop: Singularity Formation in
Nonlinear PDEs\n\n\nAbstract\nFor the Stokes system in the half space\, Ka
ng [Math.Ann.2005] showed that a solution generated by a compactly support
ed\, H\\"older continuous boundary flux may have unbounded normal derivati
ves near the boundary. We first prove explicit global pointwise estimates
of a slightly revised solution\, showing in particular that it has finite
global energy and its derivatives blow up everywhere on the boundary away
from the flux. We then use the above solution as a profile to construct so
lutions of the Navier-Stokes equations which also have finite global energ
y and unbounded normal derivatives due to the flux. Our main tool is the p
ointwise estimates of the Green tensor of the Stokes system proved by us i
n an earlier paper.\n We also examine the Stokes flows generated by dipole
bumps boundary flux\, and identify the regions where the normal derivativ
es of the solutions tend to positive or negative infinity near the boundar
y. This is a joint work with Kyungkeun Kang\, Baishun Lai and Chen-Chih La
i.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Roman (Catholic University of Chile)
DTSTART:20210928T193000Z
DTEND:20210928T200500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/14
DESCRIPTION:Title: Vortex lines in the 3D Ginzburg-Landau model of superconducti
vity\nby Carlos Roman (Catholic University of Chile) as part of BIRS w
orkshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe Ginzbu
rg-Landau model is a phenomenological description of superconductivity. A
crucial feature is the occurrence of vortex lines\, which appear above a c
ertain value of the strength of the applied magnetic field called the firs
t critical field. In this talk I will present a sharp estimate of this val
ue and report on a joint work with Etienne Sandier and Sylvia Serfaty in w
hich we study the onset of vortex lines and derive an interaction energy f
or them.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Zhan (Chinese Academy of Science)
DTSTART:20210929T150000Z
DTEND:20210929T153500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/15
DESCRIPTION:Title: On global hydrostatic approximation of hyperbolic Navier-Stok
es system with small Gevrey class 2 data\nby Ping Zhan (Chinese Academ
y of Science) as part of BIRS workshop: Singularity Formation in Nonlinear
PDEs\n\n\nAbstract\nWe study a hyperbolic version of the Navier-Stokes e
quations obtained by using Cattaneo heat transfer law instead of Fourier
law\, evolving in a thin strip $\\RR\\times (0\,\\varepsilon)$. The forma
l limit of these equations is a hyperbolic Prandtl type equation. We prov
e the existence and uniqueness of a global solution to these equations und
er a uniform smallness assumption on the data in Gevrey 2 class. Then we j
ustify the limit from the anisotropic hyperbolic Navier-Stokes system to t
he hydrostatic hyperbolic Navier-Stokes system with Gevrey 2 data. We also
exhibit smallness assumptions on the data in Gevrey 2 class\, under which
the solutions are global in time.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changyou Wang (Purdue University)
DTSTART:20210929T154000Z
DTEND:20210929T161500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/16
DESCRIPTION:Title: Partial regularity of a nematic liquid crystal flow with kine
matic transport effects\nby Changyou Wang (Purdue University) as part
of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nM
otivated by the non-corotational Beris-Edwards $Q$-tensor system modeling
the hydrodynamic of nematic liquid crystal materials\, we consider the cor
responding Ericksen vectorial model that\n Includes kinematic transport p
arameters for molecules of various shapes and show that there exists a glo
bal weak solution in dimension three\, which is smooth away from a closed
set with Hausdorff dimension at most $15/7$.\n This is a joint work with H
engrong Du.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angela Pistoia (Sapienza Università di Roma)
DTSTART:20210929T162000Z
DTEND:20210929T165500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/17
DESCRIPTION:Title: Critical Lane-Emden systems\nby Angela Pistoia (Sapienza
Università di Roma) as part of BIRS workshop: Singularity Formation in No
nlinear PDEs\n\n\nAbstract\nI will present some recent results concerning
non-degeneracy\, existence and multiplicity of solutions to a Lane-Emden c
ritical system\n obtained in collaboration with R.Frank and S.Kim.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otis Chodosh (Stanford University)
DTSTART:20210929T173000Z
DTEND:20210929T180500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/18
DESCRIPTION:Title: The p-widths of a surface\nby Otis Chodosh (Stanford Univ
ersity) as part of BIRS workshop: Singularity Formation in Nonlinear PDEs\
n\n\nAbstract\nThe p-widths of a Riemannian manifold were introduced by Gr
omov as a nonlinear version of the eigenvalues of the Laplacian (replacing
the Dirichlet energy on functions with the area functional on submanifold
s). I will discuss recent work with C. Mantoulidis (Rice) concerning the p
-widths on surfaces\, using in particular Liu—Wei’s analysis of entire
solutions to the sine-Gordon equation on the plane. In particular\, we pr
ove that the p-widths on a surface correspond to immersed geodesics (inste
ad of geodesic nets) and we compute the entire p-width spectrum of $ S^2$
yielding the constant in the Liokumovich—Marques—Neves Weyl law in thi
s dimension.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Souplet (Université Sorbonne Paris Nord)
DTSTART:20210929T181000Z
DTEND:20210929T184500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/19
DESCRIPTION:Title: Some recent Liouville type results and their applications
\nby Philippe Souplet (Université Sorbonne Paris Nord) as part of BIRS wo
rkshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe p-width
s of a Riemannian manifold were introduced by Gromov as a nonlinear versio
n of the eigenvalues of the Laplacian (replacing the Dirichlet energy on f
unctions with the area functional on submanifolds). I will discuss recent
work with C. Mantoulidis (Rice) concerning the p-widths on surfaces\, usin
g in particular Liu—Wei’s analysis of entire solutions to the sine-Gor
don equation on the plane. In particular\, we prove that the p-widths on a
surface correspond to immersed geodesics (instead of geodesic nets) and w
e compute the entire p-width spectrum of $ S^2$ yielding the constant in t
he Liokumovich—Marques—Neves Weyl law in this dimension.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christos Mantoulidis (Rice University)
DTSTART:20210929T185000Z
DTEND:20210929T192500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/20
DESCRIPTION:Title: Mean curvature flow with generic initial data\nby Christo
s Mantoulidis (Rice University) as part of BIRS workshop: Singularity Form
ation in Nonlinear PDEs\n\n\nAbstract\nWe discuss why the mean curvature f
low of generic closed surfaces in ${\\mathbb R}^3$ avoids asymptotically c
onical and non-spherical compact singularities. We also discuss why the me
an curvature flow of generic closed low-entropy hypersurfaces in ${\\mathb
b R}^4$ is smooth until it disappears in a round point. This is joint work
with O. Chodosh\, K. Choi\, and F. Schulze.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoshihiro Tonegawa (Tokyo Institute of Technology)
DTSTART:20210929T193000Z
DTEND:20210929T200500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/21
DESCRIPTION:Title: Existence of canonical multi-phase mean curvature flows\n
by Yoshihiro Tonegawa (Tokyo Institute of Technology) as part of BIRS work
shop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nI present a r
ecent existence result for multi-phase Brakke flow starting\n from arbitra
ry partition with locally finite co-dimension 1 Hausdorff measure\n which
improves on my own work with Lami Kim in 2017. The new aspect is that\n th
e flow has a character of BV solution\, a notion introduced by \n Luckhaus
-Sturzenhecker in 1995\, in addition to being a Brakke flow.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John King (Tokyo Institute of Technology)
DTSTART:20210930T150000Z
DTEND:20210930T153500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/22
DESCRIPTION:Title: Some blow-up and post-blow-up results for quasilinear reactio
n diffusion\nby John King (Tokyo Institute of Technology) as part of B
IRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nSome
formal asymptotic results will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marek Fila (Comenius University)
DTSTART:20210930T154000Z
DTEND:20210930T161500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/23
DESCRIPTION:Title: Solutions with snaking singularities for the fast diffusion e
quation\nby Marek Fila (Comenius University) as part of BIRS workshop:
Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nWe construct solut
ions of the fast diffusion equation\, which exist for\nall $t\\in {\\mathb
b R}$ and are singular on the set $\\Gamma(t):= \\{ \\xi(s) \;\ns \\leq c
t \\}$\, $c>0$\, 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 sol
utions near\n $\\Gamma(t)$. This is a joint work with John King\, Jin Tak
ahashi and Eiji\n Yanagida.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Seis (Munster University)
DTSTART:20210930T162000Z
DTEND:20210930T165500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/24
DESCRIPTION:Title: Leading order asymptotics for fast diffusion on bounded domai
ns\nby Christian Seis (Munster University) as part of BIRS workshop: S
ingularity Formation in Nonlinear PDEs\n\n\nAbstract\nOn a smooth bounded
Euclidean domain\, Sobolev-subcritical fast diffusion with vanishing boun
dary trace leads to finite-time extinction\, with a vanishing profile sele
cted by the initial datum. In rescaled variables\, we quantify the rate of
convergence to this profile uniformly in relative error\, showing the ra
te is either exponentially fast (with a rate constant predicted by the spe
ctral gap) or algebraically slow (which is only possible in the presence o
f zero modes). In the first case\, we identify the leading order asymptoti
cs. Our results improve various results in the literature\, while shorten
ing their proofs. Joint work with Beomjun Choi and Robert J. McCann.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Contreras (New Mexico State Univerity)
DTSTART:20210930T173000Z
DTEND:20210930T180500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/25
DESCRIPTION:Title: Stable vortex configurations with unbounded vorticity in Ginz
burg-Landau theory\nby Andres Contreras (New Mexico State Univerity) a
s part of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbst
ract\nIn Ginzburg-Landau theory\, the presence of a strong magnetic field
allows for the existence of stable vortex states. The study of global mini
mizers of the Ginzburg-Landau energy in $2d$ and a characterization of the
ir vorticities is the focus of a series of works by Sandier and Serfaty in
the$\\varepsilon \\to 0$ limit\, where $\\varepsilon$is the inverse of th
e Ginzburg-Landau parameter. However\, the full range of existence of stab
le configurations with prescribed vorticity\, different from the optimal o
ne\, remains an open problem. In particular\, it is expected that local mi
nimizers with $1\\ll N\\sim 1/\\varepsilon^\\alpha\,$ for some $\\alpha>0$
should exist\, provided the magnetic field is strong enough. The best par
tial results until recently could only cover very slowly diverging ($N\\le
sssim |\\log \\varepsilon|$)numbers of vortices. In joint work with R. L.
Jerrard\, we prove the existence of local minimizers with prescribed vorti
city for a wide range of external fields and treat for the first timea num
ber ofvortices comparable to a power of $1/\\varepsilon.$\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins University)
DTSTART:20210930T181000Z
DTEND:20210930T184500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/26
DESCRIPTION:Title: A new Ginzburg-Landau approximation for the heat flow of harm
onic maps with free boundary and partial regularity of weak solutions\
nby Yannick Sire (Johns Hopkins University) as part of BIRS workshop: Sing
ularity Formation in Nonlinear PDEs\n\n\nAbstract\nHarmonic maps with free
boundary are rather old objects in geometry which has been used recently
in several results related to the co-dimension one conjecture\, extremal m
etrics of Steklov eigenvalues or liquid crystal flows. I will report on re
cent results on a new approximation of these maps which allows to better c
apture the boundary behavior and construct weak solutions of the associate
d heat flow. I will also give a small energy criterion which allows to pro
ve partial regularity of the solutions.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose' Antonio Carrillo (University of Oxford)
DTSTART:20210930T185000Z
DTEND:20210930T192500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/27
DESCRIPTION:Title: Nonlocal Aggregation-Diffusion Equations: entropies\, gradien
t flows\, phase transitions and application\nby Jose' Antonio Carrillo
(University of Oxford) as part of BIRS workshop: Singularity Formation in
Nonlinear 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 fo
rmation\, optimization\, granular media\, swarming behavior\, opinion dyna
mics and financial mathematics to name a few. We will present several resu
lts related to localized Cucker-Smale orientation dynamics\, McKean-Vlasov
equations\, and nonlinear diffusion Keller-Segel type models in several s
ettings. We will show the existence of continuous or discontinuous phase t
ransitions on the torus under suitable assumptions on the Fourier modes of
the interaction potential. The analysis is based on linear stability in t
he right functional space associated to the regularity of the problem at h
and. While in the case of linear diffusion\, one can work in the L2 framew
ork\, nonlinear diffusion needs the stronger Linfty topology to proceed wi
th the analysis based on Crandall-Rabinowitz bifurcation analysis applied
to the variation of the entropy functional. Explicit examples show that th
e global bifurcation branches can be very complicated. Stability of the so
lutions will be discussed based on numerical simulations with fully explic
it energy decaying finite volume schemes specifically tailored to the grad
ient flow structure of these problems. The theoretical analysis of the asy
mptotic stability of the different branches of solutions is a challenging
open problem. This overview talk is based on several works in collaboratio
n with R. Bailo\, A. Barbaro\, J. A. Canizo\, X. Chen\, P. Degond\, R. Gva
lani\, 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 Advance
d Grant Nonlocal-CPD 883363.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liqun Zhang (Chinese Academy of Sciences)
DTSTART:20211001T142000Z
DTEND:20211001T145500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/28
DESCRIPTION:Title: The blow up solutions to Boussinesq equations on R3 with disp
ersive temperature\nby Liqun Zhang (Chinese Academy of Sciences) as pa
rt of BIRS workshop: Singularity Formation in Nonlinear PDEs\n\n\nAbstract
\nThe three-dimensional incompressible Boussinesq system is one of the imp
ortant equations in fluid dynamics. The system describes the motion of tem
perature-dependent incompressible flows. And the temperature naturally has
diffusion. Very recently\, Elgindi\, Ghoul and Masmoudi constructed a $C^
{1\,\\alpha}$ finite time blow-up solutions for Euler systems with finite
energy. Inspired by their works\, we constructed $C^{1\,\\alpha}$ finite t
ime blow-up solution for Boussinesq equations where temperature has diffus
ion and finite energy. The main difficulty is that the Laplace operator of
temperature equation is not coercive under Sobolev weighted norm which is
introduced by Elgindi. We introduced a new time scaling formulation and n
ew weighted Sobolev norms\, under which we obtain the coercivity estimate.
The new 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 Xianlia
ng.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Davila (Universiy of Bath)
DTSTART:20211001T150000Z
DTEND:20211001T153500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/29
DESCRIPTION:Title: Blow-up for the Keller-Segel system in the critical mass case
\nby Juan Davila (Universiy of Bath) as part of BIRS workshop: Singula
rity Formation in Nonlinear PDEs\n\n\nAbstract\nWe consider the Keller-Seg
el system in the plane with an initial\n condition with suitable decay and
critical mass 8 pi.\n We find a function $u_0$ with mass $8 \\pi$ such th
at\n for any initial condition sufficiently close to $u_0$ and mass $8 \\p
i$\,\n the solution is globally defined and blows up in infinite time. We
also find the\n profile and rate of blow-up. This result answers affirmati
vely the\n question of the nonradial stability raised by Ghoul and Masmoud
i\n (2018). This is joint work with Manuel del Pino (U. of Bath)\, Jean Do
lbeault (U. Paris Dauphine)\, Monica Musso (U. of Bath) and Juncheng Wei (
UBC)\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Panagiota Daskalopoulos (Columbia University)
DTSTART:20211001T154000Z
DTEND:20211001T161500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/30
DESCRIPTION:Title: Type II smoothing in Mean curvature flow\nby Panagiota Da
skalopoulos (Columbia University) as part of BIRS workshop: Singularity Fo
rmation in Nonlinear PDEs\n\n\nAbstract\nIn 1994 Velázquez constructed a
smooth \\( O(4)\\times O(4)\\) invariant\n Mean Curvature Flow that form
s a type-II singularity at the origin in\n space-time. Stolarski very r
ecently showed that the mean curvature\n on this solution is uniformly bo
unded. Earlier\, Velázquez also provided\n formal asymptotic expansions
for a possible smooth continuation of the\n solution after the singulari
ty. \n Jointly with S. Angenent and N. Sesum we establish the short tim
e existence of Velázquez' formal \n continuation\, and we verify that t
he mean curvature is also uniformly bounded on the continuation.\n Combin
ed with the earlier results of Velázquez--Stolarski we therefore show\n
that there exists a solution \\(\\{M_t^7\\subset\\RR^8 \\mid -t_0 Two non-conventional inequalities\nby Jean Dolbeault (Uni
versité Paris-Dauphine) as part of BIRS workshop: Singularity Formation i
n Nonlinear PDEs\n\n\nAbstract\nThis lecture is devoted to two inequalitie
s:\n (1) Reverse Hardy-Littlewood-Sobolev inequalities\,\n (2) Two-dimensi
onal logarithmic inequalities.\n None of these inequalities is classical.
Both raise interesting open questions\,\n with applications to nonlinear d
iffusions and Schroödinger equations\n This corresponds to joint results
obtained with: (1) Jose A. Carrillo\, Matias G. Delgadino\, Rupert L. Fran
k\, Franca Hoffmann (2) Rupert L. Frank\, Louis Jeanjean.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slim Ibrahim (University of Victoria)
DTSTART:20211001T173000Z
DTEND:20211001T180500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/32
DESCRIPTION:Title: Revisit singularity formation for the inviscid primitive equa
tion\nby Slim Ibrahim (University of Victoria) as part of BIRS worksho
p: Singularity Formation in Nonlinear PDEs\n\n\nAbstract\nThe primitive eq
uation is an important model for large scale fluid model including oceans
and atmosphere. While solutions to the viscous model enjoy global regulari
ty\, inviscid solutions may develop singularities in finite time. In this
talk\, I will review the methods to show blowup\, and case share more rece
nt progress on qualitative properties of singularity formation.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (Kelei Wang) (University of British Columbia)
DTSTART:20211001T181000Z
DTEND:20211001T184500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/33
DESCRIPTION:Title: Nonexistence of Type II blowups for an energy critical nonlin
ear heat equation\nby Juncheng Wei (Kelei Wang) (University of British
Columbia) as part of BIRS workshop: Singularity Formation in Nonlinear PD
Es\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 $n\\g
eq 7$ and $ u_0\\geq 0$\, then any blow-up must be of Type I. (In the rad
ially symmetric case\, $n\\geq 5$). The proof uses some ideas from geomet
ric measure theory and a reverse inner-outer gluing mechanism.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanghua Lin (New York University)
DTSTART:20211001T185000Z
DTEND:20211001T192500Z
DTSTAMP:20260404T042246Z
UID:BIRS-21w5503/34
DESCRIPTION:Title: Relaxed Energies\, Defect measures and Minimal Currents ↓\nby Fanghua Lin (New York University) as part of BIRS workshop: Singula
rity Formation in Nonlinear PDEs\n\n\nAbstract\nAfter a brief discussion f
or harmonic 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\, mi
nimal connection and some results in the late 1980s by several groups. We
then focus on a higher dimensional version of these studies. And we shal
l present a solution to an open problem proposed by Brezis-Mironescu recen
tly.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5503/34/
END:VEVENT
END:VCALENDAR