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BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State University)
DTSTART:20210726T150000Z
DTEND:20210726T155000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/1
DESCRIPTION:Title: Global existence for the 2D Kuramoto-Sivashinsky equation\
nby Anna Mazzucato (Penn State University) as part of BIRS workshop: New M
echanisms for Regularity\, Singularity\, and Long Time Dynamics in Fluid E
quations\n\n\nAbstract\nI will present recent results concerning global ex
istence for the Kuramoto-Sivashinsky equation in 2 space dimensions with a
nd without advection in the presence of growing modes. The KSE is a model
of long-wave instability in dissipative systems.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Hou (California Institute of Technology)
DTSTART:20210726T161000Z
DTEND:20210726T170000Z
DTSTAMP:20260404T042147Z
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 (
California Institute of Technology) as part of BIRS workshop: New Mechanis
ms for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equation
s\n\n\nAbstract\nWhether the 3D incompressible Euler and Navier-Stokes equ
ations can develop a finite time singularity from smooth initial data is o
ne of the most challenging problems in nonlinear PDEs. In an effort to pro
vide a rigorous proof of the potential Euler singularity revealed by Luo-H
ou's computation\, we develop a novel method of analysis and prove that th
e original De Gregorio model and the Hou-Lou model develop a finite time s
ingularity from smooth initial data. Using this framework and some techniq
ues from Elgindi's recent work on the Euler singularity\, we prove the fin
ite time blowup of the 2D Boussinesq and 3D Euler equations with $C^{1\,\\
alpha}$ initial velocity and boundary. Further\, we present some new numer
ical evidence that the 3D incompressible Euler equations with smooth initi
al data develop a potential finite time singularity at the origin\, which
is quite different from the Luo-Hou scenario. Our study also shows that t
he 3D Navier-Stokes equations develop nearly singular solutions with maxim
um vorticity increasing by a factor of $10^7$. However\, the viscous effec
t eventually dominates vortex stretching and the 3D Navier-Stokes equation
s narrowly escape finite-time blowup. Finally\, we present strong numeric
al evidence that the 3D Navier-Stokes equations with slowly decaying visco
sity develop a finite time singularity.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Nahmod (University of Massachusetts)
DTSTART:20210726T192000Z
DTEND:20210726T201000Z
DTSTAMP:20260404T042147Z
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 BIR
S workshop: New Mechanisms for Regularity\, Singularity\, and Long Time Dy
namics in Fluid Equations\n\n\nAbstract\nWe review recent work\, joint wi
th Yu Deng and Haitian Yue\, about the Gibbs measure for the periodic 2D N
LS and 3D Hartree NLS as well as the theory of random tensors\, a powerfu
l new framework which allows us to unravel the propagation of randomness u
nder the nonlinear flow beyond the linear evolution of random data. This e
nables us in particular\, to show the existence and uniqueness of solution
s to the periodic NLS in an optimal range relative to what we define as th
e probabilistic scaling.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shkoller (UC Davis)
DTSTART:20210726T203000Z
DTEND:20210726T212000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/4
DESCRIPTION:Title: Simultaneous development of shocks and cusps for 2D compressib
le Euler from smooth initial data\nby Steve Shkoller (UC Davis) as par
t of BIRS workshop: New Mechanisms for Regularity\, Singularity\, and Long
Time Dynamics in Fluid Equations\n\n\nAbstract\nA fundamental question in
fluid dynamics concerns the formation of discontinuous shock waves from s
mooth initial data. We first classify the first singularity\, the so-cal
led $C^{\\frac{1}{3}} $ pre-shock\, as a fractional series expansion with
coefficients computed from the data. With this precise pre-shock descript
ion\, we prove that a discontinuous shock instantaneously develops after
the pre-shock. This regular shock solution is shown to be unique in a cla
ss 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 emer
ge from the pre-shock. We prove that along the slowest surface\, all f
luid variables 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 direction of its motion\; we thus term this surface a weak rarefacti
on wave. Along the surface moving with the fluid velocity\, density and e
ntropy form $C^{1\, {\\frac{1}{2}} }$ one-sided cusps while the pressure a
nd normal velocity remain $C^2$\; as such\, we term this surface a weak c
ontact discontinuity.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yan Guo (Brown University)
DTSTART:20210727T150000Z
DTEND:20210727T155000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/5
DESCRIPTION:Title: Dynamics of Contact Line\nby Yan Guo (Brown University) as
part of BIRS workshop: New Mechanisms for Regularity\, Singularity\, and
Long Time Dynamics in Fluid Equations\n\n\nAbstract\nContact lines (e.g\,
where coffee meets the coffee cup or a droplet)\nappear generically betwee
n a free surface and a fixed boundary. Even\nthough the steady contact lin
e and contact angle was studied by people\nlike Gauss and Young\, even the
modelling of dynamic contact lines has\nbeen an active research area in p
hysics. In a joint research program\ninitiated with Ian Tice\, global well
-posedness and stability of\ncontact lines is established for a recent vis
cous fluid model in 2D.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (University of California - Los Angeles)
DTSTART:20210727T161000Z
DTEND:20210727T170000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/6
DESCRIPTION:Title: Universality and possible blowup in fluid equations\nby Te
rence Tao (University of California - Los Angeles) as part of BIRS worksho
p: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics in
Fluid Equations\n\n\nAbstract\nWe discuss some possible (and still specul
ative) routes to establishing finite time blowup in fluid equations (and o
ther PDE)\, focusing in particular on methods based on establishing univer
sality properties for such equations.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nader Masmoudi (Courant Institute and NYUAD)
DTSTART:20210727T173000Z
DTEND:20210727T182000Z
DTSTAMP:20260404T042147Z
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://stable.researchseminars.org/talk/BIRS-21w5110/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Deng (University of Southern California)
DTSTART:20210727T192000Z
DTEND:20210727T201000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/8
DESCRIPTION:Title: Full derivation of the wave kinetic equation\nby Yu Deng (
University of Southern California) as part of BIRS workshop: New Mechanism
s for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations
\n\n\nAbstract\nThe wave kinetic equation is a central topic in the theory
of wave turbulence\, which concerns the thermodynamic limit of interactin
g wave systems. It can be traced back to the 1920s and has played signific
ant roles in different areas of physics. However\, the mathematical justif
ication of the theory has long been open. In this talk we present our rece
nt work\, which resolves this problem by providing the rigorous derivation
of the wave kinetic equation. This is joint work with Zaher Hani (Univers
ity of Michigan).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juhi Jang (University of Southern California)
DTSTART:20210727T203000Z
DTEND:20210727T212000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/9
DESCRIPTION:Title: Gravitational Collapse for Newtonian Stars\nby Juhi Jang (
University of Southern California) as part of BIRS workshop: New Mechanism
s for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations
\n\n\nAbstract\nA classical model to describe the dynamics of Newtonian st
ars is the gravitational Euler-Poisson system. The Euler-Poisson system ad
mits a wide range of star solutions that are in equilibrium or expand for
all time or collapse in a finite time or rotate. In this talk\, I will dis
cuss some recent progress on those star solutions with focus on gravitatio
nal collapse. The talk is based on joint works with Yan Guo and Mahir Hadz
ic.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yao Yao (Georgia Tech)
DTSTART:20210728T150000Z
DTEND:20210728T155000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/10
DESCRIPTION:Title: Small scale formations in the incompressible porous media equ
ation\nby Yao Yao (Georgia Tech) as part of BIRS workshop: New Mechani
sms for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equatio
ns\n\n\nAbstract\nThe incompressible porous media (IPM) equation describes
the evolution of density transported by an incompressible velocity field
given by Darcy’s law. Here the velocity field is related to the density
via a singular integral operator\, which is analogous to the 2D SQG equati
on. The question of global regularity vs finite-time blow-up remains open
for smooth initial data\, although numerical evidence suggests that small
scale formation can happen as time goes to infinity. In this talk\, I will
discuss rigorous examples of small scale formations in the IPM equation:
we construct solutions to IPM that exhibit infinite-in-time growth of Sobo
lev norms\, provided that they remain globally smooth in time. As an appli
cation\, this allows us to obtain nonlinear\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Constantin (Princeton University)
DTSTART:20210728T161000Z
DTEND:20210728T170000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/11
DESCRIPTION:Title: Nernst-Planck-Navier-Stokes Equations\nby Peter Constanti
n (Princeton University) as part of BIRS workshop: New Mechanisms for Regu
larity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbst
ract\nThe Nernst-Planck-Navier-Stokes equations model the evolution of ion
s\nin Newtonian fluids. I will describe results on global existence and\ns
tability of smmoth solutions and on asymptotic interior electroneutrality\
n(the vanishing of the charge density away from boundaries\, in the limit
of zero Debye\nscreening length). The talk is based on recent works with M
. Ignatova and with F-N\nLee.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrej Zlatos (University of California San Diego)
DTSTART:20210728T192000Z
DTEND:20210728T201000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/12
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby Andrej Zlat
os (University of California San Diego) as part of BIRS workshop: New Mech
anisms for Regularity\, Singularity\, and Long Time Dynamics in Fluid Equa
tions\n\n\nAbstract\nBounded vorticity solutions to the 2D Euler equations
on singular domains are typically not close to Lipschitz near boundary si
ngularities\, which makes their uniqueness a difficult open problem. I wi
ll present a general sufficient condition on the geometry of the domain th
at guarantees global uniqueness for all solutions initially constant near
the boundary. This condition is only slightly more restrictive than exclu
sion of corners with angles greater than $\\pi$ and\, in particular\, is s
atisfied by all convex domains. Its proof is based on showing that fluid
particle trajectories for general bounded vorticity solutions cannot reach
the boundary in finite time. The condition also turns out to be sharp in
the latter sense: there are domains that come arbitrarily close to satisf
ying it and on which particle trajectories can reach the boundary in finit
e time.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sverak (University of Minnesota)
DTSTART:20210728T203000Z
DTEND:20210728T212000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/13
DESCRIPTION:Title: Euler Equations on General Planar Domains\nby Vladimir Sv
erak (University of Minnesota) as part of BIRS workshop: New Mechanisms fo
r Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n
\nAbstract\nWe discuss the first few terms in the asymptotic expansion of
the solutions of $-\\Delta u + u\\nabla u+\\nabla p=f(x)$ at infinity (ass
uming $f(x)$ is localized and not too large). The first term has been know
n for some time and is given by Landau solutions. The higher-order terms
exhibit interesting behavior. \nJoint work with Hao Jia.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Constantin (Vienna University)
DTSTART:20210729T150000Z
DTEND:20210729T155000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/14
DESCRIPTION:Title: Large-amplitude steady downstream water waves\nby Adrian
Constantin (Vienna University) as part of BIRS workshop: New Mechanisms fo
r Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n
\nAbstract\nA study of wave-current interactions in two-dimensional\nwater
flows of constant vorticity over a flat bed is discussed.\nFor large-ampl
itude periodic traveling waves that propagate at\nthe water surface in the
same direction as the underlying current\n(downstream waves)\, we prove e
xplicit uniform bounds for their\namplitude. In particular\, our estimates
show that the maximum\namplitude of the waves becomes vanishingly small a
s the vorticity\nincreases without limit. We also prove that the downstrea
m waves\non a global bifurcating branch are never overhanging\, and that t
heir\nmass flux and Bernoulli constant are uniformly bounded. This is\njoi
nt work with Walter Strauss (Brown University\, USA) and Eugen\nVarvaruca
(University of Iasi\, Romania).\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Musso (University of Bath)
DTSTART:20210729T161000Z
DTEND:20210729T170000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/15
DESCRIPTION:Title: Solutions of the incompressible Euler equations with concentr
ated vorticity\nby Monica Musso (University of Bath) as part of BIRS w
orkshop: New Mechanisms for Regularity\, Singularity\, and Long Time Dynam
ics in Fluid Equations\n\n\nAbstract\nI will discuss solutions to the inco
mpressible Euler equation in two di-mensions with vorticity close to a fin
ite sum of Dirac deltas (vortices). The law of motion of the vortices was
known formally for a long time and proved rigorously by Marchioro-Pulviren
ti. 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 constru
ction can be generalized to other situations\,such as the construction of
leapfrogging vortex rings of the 3D incompressibleEuler equations.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigory Seregin (Oxford University)
DTSTART:20210729T173000Z
DTEND:20210729T182000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/16
DESCRIPTION:Title: Local regularity of axisymmetric solutions to Navier-Stokes e
quations\nby Grigory Seregin (Oxford University) as part of BIRS works
hop: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics
in Fluid Equations\n\n\nAbstract\nThe aim of our talk is to show that axia
lly symmetric suitable weak solutions to the Navier-Stokes equations have
no Type I blowups. This can be done by reduction to a Liouville type theor
em for a certain governing equation on a scalar function.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tai-Peng Tsai (University of British Columbia)
DTSTART:20210729T192000Z
DTEND:20210729T201000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/17
DESCRIPTION:Title: Local regularity conditions on initial data for local energy
solutions of the Navier-Stokes equations\nby Tai-Peng Tsai (University
of British Columbia) as part of BIRS workshop: New Mechanisms for Regular
ity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\n\nAbstrac
t\nWe show local regularity of local energy solutions to the Navier-Stokes
equations in terms of local scaled integrals of the initial data. It exte
nds previous work of Jia-Sverak\, Barker-Prange and ourselves. This refine
d criterion implies that if a weighted $L^2$ norm of the initial data is f
inite\, then all local energy solutions are regular in a region confined b
y space-time hypersurfaces determined by the weight. This result generali
zes Theorems C and D of Caffarelli\, Kohn and Nirenberg (Comm. Pure Appl.
Math. 35\; 1982). This is a joint work with Kyungkeun Kang and Hideyuki Mi
ura.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benoit Pausader (Brown University)
DTSTART:20210729T203000Z
DTEND:20210729T212000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/18
DESCRIPTION:Title: Long time existence for the Euler-Coriolis system\nby Ben
oit Pausader (Brown University) as part of BIRS workshop: New Mechanisms f
or Regularity\, Singularity\, and Long Time Dynamics in Fluid Equations\n\
n\nAbstract\nThis is a joint work with Y. Guo and K. Widmayer. We consider
the Euler equation in 3d with a Coriolis force and we show that small\, s
mooth and localized initial data which are axisymmetric lead to solutions
which exist 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 quasilinear dispersive equations.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gomez Serrano (Brown University)
DTSTART:20210730T150000Z
DTEND:20210730T155000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/19
DESCRIPTION:Title: Symmetry in stationary and uniformly rotating solutions of fl
uid equations\nby Javier Gomez Serrano (Brown University) as part of B
IRS workshop: New Mechanisms for Regularity\, Singularity\, and Long Time
Dynamics in Fluid Equations\n\n\nAbstract\nIn this talk\, I will discuss c
haracterizations of stationary or uniformly-rotating solutions of 2D Euler
and other similar equations. The main question we want to address is whet
her every stationary/uniformly-rotating solution must be radially symmetri
c. Based on joint work with Jaemin Park\, Jia Shi and Yao Yao.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabio Pusateri (University of Toronto)
DTSTART:20210730T161000Z
DTEND:20210730T170000Z
DTSTAMP:20260404T042147Z
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://stable.researchseminars.org/talk/BIRS-21w5110/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20210730T192000Z
DTEND:20210730T201000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/21
DESCRIPTION:Title: Finite time singularities for some fluid-related equations\nby Juncheng Wei (University of British Columbia) as part of BIRS worksh
op: New Mechanisms for Regularity\, Singularity\, and Long Time Dynamics i
n Fluid Equations\n\n\nAbstract\nI will report some recent results on the
existence of finite time blow-up for nematic liquid crystal flows and Land
au-Lipschitz-Gilbert equation. The nematic liquid crystal flow is a coupl
ed system of harmonic map flows and Navier-Stokes system while LLG is a st
andard model in magnetics. I will show how the gluing techniques can be a
pplied to both equations to produce blow-ups.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Vasseur (University of Texas at Austin)
DTSTART:20210730T203000Z
DTEND:20210730T212000Z
DTSTAMP:20260404T042147Z
UID:BIRS-21w5110/22
DESCRIPTION:Title: Instability of finite time blow-ups for incompressible Euler<
/a>\nby Alexis Vasseur (University of Texas at Austin) 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\, we will discuss the int
eraction between the stability\, and the propagation of regularity\, for s
olutions to the incompressible 3D Euler equation. It is still unknown whet
her a solution with smooth initial data can develop a singularity in finit
e time. We will describe how\, in such a scenario\, the solution becomes u
nstable as time approaches the blow-up time. The method uses the relation
between the vorticity of the solution\, and the bi-characteristic amplitud
e solutions\, which describe the evolution of the linearized Euler equatio
n at high frequency. In the axisymmetric case\, we can also study the inst
ability of blow-up profiles. This work was partially supported by the NSF
DMS-1907981. This a joint work with Misha Vishik and Laurent Lafleche.\n
LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5110/22/
END:VEVENT
END:VCALENDAR