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BEGIN:VEVENT
SUMMARY:Sergei KUKSIN (University Paris 7 Diderot)
DTSTART:20200930T140000Z
DTEND:20200930T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/1
DESCRIPTION:Title: Kolmogorov theory of turbulence and its rigorous model\, given by
the Burgers equation\nby Sergei KUKSIN (University Paris 7 Diderot) a
s part of Dynamical systems and PDEs\n\n\nAbstract\nI will present three m
ain laws from the Kolmogorov theory of turbulence ("the K41 model")\, disc
uss their versions for one-dimensional fluid and will show that the latter
may be rigorously justified for the 1d fluid\, described by the Burgers e
quation\, via a qualitative analysis of the dynamical system which the equ
ation defines in Sobolev spaces. The talk is based on a MS of my joint boo
k with Alex Boritchev.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela PROCESI (Università degli Studi Roma Tre)
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/2
DESCRIPTION:Title: Some new results on almost periodic solutions for dispersive PDEs
on the circle\nby Michela PROCESI (Università degli Studi Roma Tre)
as part of Dynamical systems and PDEs\n\n\nAbstract\nExistence of almost p
eriodic solutions for evolution PDEs is a very interesting problem\, with
a lot of open questions. Most of the literature is on the construction of
very regular solutions for semilinear PDEs (mainly the NLS) with external
parameters. I shall discuss two new results: 1. existence of solutions for
a quasi-linear forced Airy equation\, 2. existence of finite regularity s
olutions for the traslation invariant NLS equation.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei TABACHNIKOV (Pennsylvania State University)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/3
DESCRIPTION:Title: Flavors of bicycle mathematics\nby Sergei TABACHNIKOV (Pennsy
lvania State University) as part of Dynamical systems and PDEs\n\n\nAbstra
ct\nThis talk concerns a naive model of bicycle motion: a bicycle is a seg
ment of fixed length that can move so that the velocity of the rear end is
always aligned with the segment. Surprisingly\, this simple model is quit
e rich and has connections with several areas of research\, including comp
letely integrable systems. Here is a sampler of problems that I hope to to
uch upon:\n1) The trajectory of the front wheel and the initial position o
f the bicycle uniquely determine its motion and its terminal position\; th
e monodromy map sending the initial position to the terminal one arises. T
his mapping is a Moebius transformation\, a remarkable fact that has vario
us geometrical and dynamical consequences.\n2) The rear wheel track and a
choice of the direction of motion uniquely determine the front wheel track
\; changing the direction to the opposite\, yields another front track. Th
ese two front tracks are related by the bicycle (Backlund\, Darboux) corre
spondence\, which defines a discrete time dynamical system on the space of
curves. This system is completely integrable and it is closely related wi
th another\, well studied\, completely integrable dynamical system\, the f
ilament (a.k.a binormal\, smoke ring\, local induction) equation.\n3) Give
n the rear and front tracks of a bicycle\, can one tell which way the bicy
cle went? Usually\, one can\, but sometimes one cannot. The description of
these ambiguous tire tracks is an open problem\, intimately related with
Ulam's problem in flotation theory (in dimension two): is the round ball t
he only body that floats in equilibrium in all positions? This problem is
also related to the motion of a charge in a magnetic field of a special ki
nd. It turns out that the known solutions are solitons of the planar versi
on of the filament equation.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Denisov (University of Wisconsin-Madison)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/4
DESCRIPTION:Title: Singularity formation in the contour dynamics for 2d Euler equati
on on the plane\nby Sergey Denisov (University of Wisconsin-Madison) a
s part of Dynamical systems and PDEs\n\n\nAbstract\nWe will study 2d Euler
dynamics of centrally symmetric pair of patches on the plane. In the pres
ence of exterior regular velocity\, we will show that these patches can me
rge so fast that the distance between them allows double-exponential upper
bound which is known to be sharp. The formation of the 90 degree corners
on the interface and the self-similarity analysis of this process will be
discussed. For a model equation\, we will discuss existence of the curve o
f smooth stationary solutions that originates at singular stationary stead
y state.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Niederman (University Paris-Saclay)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/5
DESCRIPTION:Title: Quasi periodic co-orbital motions (joint work with Philippe Robu
tel and Alexandre Pousse)\nby Laurent Niederman (University Paris-Sacl
ay) as part of Dynamical systems and PDEs\n\n\nAbstract\nThe motions of th
e satellites Janus and Epimetheus around Saturn are among the most intrigu
ing in the solar system since they exchange their orbits every four years.
\n\nIn [1]\, we give a rigorous proof of the existence of quasi-periodic o
rbits (hence stable) which exhibit this exchange property in the three bod
y plane planetary problem thanks to KAM theory.\n\n[1] On the Co-orbital M
otion in the Three-Body Problem: Existence of Quasi-periodic Horseshoe-Sha
ped Orbits\, L. Niederman\, A. Pousse\, P. Robutel\, Comm. Math. Phys.\, v
ol. 377\, pp. 551–612 (2020)\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Polterovich (Tel Aviv University)
DTSTART:20201223T150000Z
DTEND:20201223T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/6
DESCRIPTION:Title: Instabilities in Hamiltonian dynamics and symplectic topology
\nby Leonid Polterovich (Tel Aviv University) as part of Dynamical systems
and PDEs\n\n\nAbstract\nI outline an existence mechanism\, based on sympl
ectic topology\, for orbits of Hamiltonian flows connecting a pair of disj
oint subsets in the phase space. Applications include "superconductivity c
hannels" in nearly integrable systems\, and contact dynamics (joint with M
ichael Entov).\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (École Normale Supérieure)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/7
DESCRIPTION:Title: On the derivation of the Boltzmann equation: fluctuations and lar
ge deviations\nby Isabelle Gallagher (École Normale Supérieure) as p
art of Dynamical systems and PDEs\n\n\nAbstract\nIt has been known since L
anford’s result in 1974 that in the limit when the number of particles g
oes to infinity in a rarefied gas\, the one-particle distribution satisfie
s the Boltzmann equation\, at least for a short time. In this talk we shal
l analyze the fluctuations\, and large deviations around that limit. This
corresponds to joint works with Thierry Bodineau\, Laure Saint-Raymond and
Sergio Simonella.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Novikov (École Polytechnique\, France & IEPT RAS\, Russia)
DTSTART:20210210T150000Z
DTEND:20210210T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/8
DESCRIPTION:Title: Multidimensional inverse scattering problem for the Schrödinger
equation\nby Roman Novikov (École Polytechnique\, France & IEPT RAS\
, Russia) as part of Dynamical systems and PDEs\n\n\nAbstract\nWe give a s
hort review of old and recent results on the multidimensional inverse scat
tering problem for the Schrödinger equation.\nA special attention is paid
to efficient reconstructions of the potential from scattering data which
can be measured in practice.\nPotential applications include phaseless inv
erse X-ray scattering\, acoustic tomography and tomographies using element
ary particles.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Kleptsyn (Institute of Mathematical Research of Rennes)
DTSTART:20210224T150000Z
DTEND:20210224T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/9
DESCRIPTION:Title: The Furstenberg theorem : adding a parameter and removing the sta
tionarity (on a joint work with A. Gorodetski)\nby Victor Kleptsyn (In
stitute of Mathematical Research of Rennes) as part of Dynamical systems a
nd PDEs\n\n\nAbstract\nThe classical Furstenberg theorem describes the (al
most sure) behaviour of a random product of independent matrices from SL(n
\,R)\; their norms turn out to grow exponentially. In our joint work\, we
study what happens if the random matrices from SL(2\,R) depend on an addit
ional parameter. It turns out that in this new situation\, the conclusion
changes. Namely\, under some natural conditions\, there almost surely exis
ts a (random) "exceptional" set on parameters where the lower limit for th
e Lyapunov exponent vanishes.\nAnother direction of the generalization of
the classical Furstenberg theorem is removing the stationarity assumption.
That is\, the matrices that are multiplied are still independent\, but no
longer identically distributed. Though in this setting most of the standa
rd tools are no longer applicable (no more stationary measure\, no more Bi
rkhoff ergodic theorem\, etc.)\, it turns out that the Furstenberg theorem
can (under the appropriate assumptions) still be generalized to this sett
ing\, with a deterministic sequence replacing the Lyapunov exponent. These
two generalizations can be mixed together\, providing the Anderson locali
zation conclusions for the non-stationary 1D random Schrodinger operators.
\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Stolovitch (University of Côte d'Azur)
DTSTART:20210310T150000Z
DTEND:20210310T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/10
DESCRIPTION:Title: Geometry of hyperbolic Cauchy-Riemann singularities and KAM-like
theory for holomorphic involutions\nby Laurent Stolovitch (University
of Côte d'Azur) as part of Dynamical systems and PDEs\n\n\nAbstract\nIn
this talk\, we emphasize how the understanding of the properties of some d
ynamical systems can lead to the understandings of some (a priori unrelate
d) geometric problems.\n\nTo be more specific\, we shall give some new ins
ights of the geometry of germs of real analytic surfaces in (C^2\,0) havin
g an isolated Cauchy-Riemann (CR) singularity at the origin. These are per
turbations of Bishop quadrics. There are two kinds of CR singularities sta
ble under perturbations: elliptic and hyperbolic. Elliptic case was studie
d by Moser-Webster in their seminal '83 article\, where they showed that s
uch a surface is locally\, near the CR singularity\, holomorphically equiv
alent to normal form from which lots of geometric/analytic features can be
read off.\n\nHere\, we focus on perturbations of hyperbolic quadrics. As
was shown by Moser-Webster\, such a surface can be transformed to a formal
normal form by a formal change of coordinates that may not be holomorphic
in any neighborhood of the origin.\nGiven a non-degenerate real analytic
surface M in (C^2\,0) having a hyperbolic CR singularity at the origin\,
we prove the existence of Whitney smooth family of holomorphic curves int
ersecting M along holomorphic hyperbolas. This is the very first result co
ncerning hyperbolic CR singularity not equivalent to quadrics.\n \n This
is a consequence of a non-standard KAM-like theorem for pair of germs of
holomorphic involutions $\\{\\tau_1\,\\tau_2\\}$ at the origin\, a common
fixed point. We show that such a pair has large amount of invariant analyt
ic sets biholomorphic to $\\{z_1z_2=const\\}$ (which is not the usual toru
s) in a neighborhood of the origin\, and that they are conjugate to restri
ctions of linear maps on such invariant sets. This is a joint work with Z.
Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Veselov (Loughborough University\, UK\; Moscow State Uni
versity and Steklov Mathematical Institute\, Russia)
DTSTART:20210324T150000Z
DTEND:20210324T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/11
DESCRIPTION:Title: Geodesic scattering on hyperboloids and Knoerrer’s map\nby
Alexander Veselov (Loughborough University\, UK\; Moscow State University
and Steklov Mathematical Institute\, Russia) as part of Dynamical systems
and PDEs\n\n\nAbstract\nGeodesic flow on ellipsoids is one of the most ce
lebrated classical integrable systems considered by Jacobi in 1837. Moser
revisited this problem in 1978 revealing the link with the modern theory o
f solitons. Surprisingly a similar question for hyperboloids did not get m
uch attention\, although the dynamics in this case is very different.\n\nI
will explain how to use the remarkable results of Moser and Knoerrer on t
he relations between Jacobi problem and integrable Neumann system on spher
e to describe explicitly the geodesic scattering on hyperboloids. It will
be shown also that Knoerrer's reparametrisation is closely related to the
projectively equivalent metric on a quadric discovered in 1998 by Tabachni
kov and\, independently\, by Matveev and Topalov\, giving a new proof of t
heir result. The projectively equivalent metric (in contrast to the usual
one) turns out to be regular on the projective closure of hyperboloid\, wh
ich allows us to extend Knoerrer's map to this closure. \n\nThe talk is ba
sed on a recent joint work with Lihua Wu.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilhelm Schlag (Yale University)
DTSTART:20210407T140000Z
DTEND:20210407T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/12
DESCRIPTION:Title: On the long-term dynamics of nonlinear wave equations and the un
iqueness of solitons\nby Wilhelm Schlag (Yale University) as part of D
ynamical systems and PDEs\n\n\nAbstract\nWe will discuss the problem of ex
istence and uniqueness of nonzero solutions of finite energy to semilinear
elliptic PDEs. The uniqueness question\, which is often delicate\, has co
nsequences for the spectral properties of the linearized operators. This i
n turn is of essence for the long-term dynamics of solutions. In particula
r\, I will describe recent work with Alex Cohen and Kevin Li at Yale on th
e long-standing problem of uniqueness of the first few excited states for
the cubic problem in three dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Huveneers (University Paris-Dauphine)
DTSTART:20210421T140000Z
DTEND:20210421T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/13
DESCRIPTION:Title: Integrability breaking in extended Hamiltonian systems\nby F
rancois Huveneers (University Paris-Dauphine) as part of Dynamical systems
and PDEs\n\n\nAbstract\nIn low dimensional Hamiltonian systems\, several
classical results such as the KAM theorem or Nekhoroshev estimates guarant
ee that the dynamics remains close to integrable in the vicinity of an int
egrable point. In statistical physics and thermodynamics\, one needs to co
nsider extensive systems at positive temperature. In this case\, the commo
n belief is that integrability is completely lost as soon as one leaves th
e integrable limit. Nevertheless\, as we will see in this talk\, the dynam
ics on some intermediate time scales may be strongly affected by integrabl
e effects. The understanding of the dynamics on such timescales is directl
y relevant to evaluate the thermal or electrical conductivity.\n\nThe talk
will consist of two parts: First\, I will introduce the topic\, describe
the phenomenology and state a few mathematical results that we obtained in
the last years (works with W. De Roeck). Second\, I will discuss the Gree
n-Kubo formula for the conductivity and I will present some open problems
related to our results.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Bambusi (University of Milan)
DTSTART:20210512T140000Z
DTEND:20210512T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/14
DESCRIPTION:Title: Growth of Sobolev norms for unbounded perturbations of the Lapla
cian on flat tori (towards a quantum Nekhoroshev theorem)\nby Dario B
ambusi (University of Milan) as part of Dynamical systems and PDEs\n\n\nAb
stract\nI will present a study of the time dependent Schr\\"odinger\nequat
ion\n$$ -i\\psi_t=-\\Delta\\psi+{\\cal V}(t\,x\,-i\\nabla)\\psi\n$$\non a
flat $d$ dimensional torus. Here ${\\cal V}$ is a time dependent\npseudodi
fferential operator of order strictly smaller than 2. The main result I wi
ll give is an estimate\nensuring that the Sobolev norms of the solutions a
re bounded by\n$t^{\\epsilon}$. The proof is a quantization of the proof o
f the\nNekhoroshev theorem\, both analytic and geometric parts.\n\nPreviou
s results of this kind were limited either to the case of\nbounded perturb
ations of the Laplacian or to quantization of systems\nwith a trivial geom
etry of the resonances\, lik harmonic oscillators or\n1-d systems. \n\nIn
this seminar I will present the result and the main ideas of the\nproof. \
n\nThis is a joint work with Beatrice Langella and Riccardo Montalto.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART:20210526T140000Z
DTEND:20210526T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/15
DESCRIPTION:Title: A regularity method for lower bounds on the Lyapunov exponent fo
r stochastic differential equations\nby Jacob Bedrossian (University o
f Maryland) as part of Dynamical systems and PDEs\n\n\nAbstract\nIn a rece
nt joint work with Alex Blumenthal and Sam Punshon-Smith\, we put forward
a new method for obtaining quantitative lower bounds on the top Lyapunov e
xponent of stochastic differential equations (SDEs). Our method combines (
i) an (apparently new) identity connecting the top Lyapunov exponent to a
degenerate Fisher information-like functional of the stationary density of
the Markov process tracking tangent directions with (ii) a quantitative v
ersion of Hörmander’s hypoelliptic regularity theory in an L1 framework
which estimates this Fisher information from below by a fractional Sobole
v norm using the Kolmogorov equation.. As an initial application\, we prov
e the positivity of the top Lyapunov exponent for a class of weakly-dissip
ative\, weakly forced SDE and that this class includes the Lorenz 96 model
in any dimension greater than or equal to 7 (as well as finite-dimensiona
l truncations of shell models GOY and SABRA). This is the first mathematic
ally rigorous proof of chaos (in the sense of positive Lyapunov exponents)
for stochastically driven Lorenz 96\, despite the overwhelming numerical
evidence (the deterministic case remains far out of reach).\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Mironov (Sobolev Institute of Mathematics)
DTSTART:20210609T140000Z
DTEND:20210609T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/16
DESCRIPTION:Title: Commuting differential and difference operators\nby Andrey M
ironov (Sobolev Institute of Mathematics) as part of Dynamical systems and
PDEs\n\n\nAbstract\nWe will discuss the connection between commuting ordi
nary differential operators and commuting difference operators. In particu
lar\, we construct a discretization of the Lamé operator that preserves t
he spectral curve.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Faou (INRIA-Rennes & IRMAR University of Rennes)
DTSTART:20210929T140000Z
DTEND:20210929T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/17
DESCRIPTION:Title: Linear damping around inhomogeneous stationary states of the Vla
sov-HMF model\nby Erwan Faou (INRIA-Rennes & IRMAR University of Renne
s) as part of Dynamical systems and PDEs\n\n\nAbstract\nWe will consider t
he dynamics of perturbations around an inhomogeneous stationary state of t
he Vlasov-HMF (Hamiltonian Mean-Field) model\, satisfying a linearized sta
bility criterion. Such stationary states are closely related to the dynami
cs of the pendulum system. We consider solutions of the linearized equatio
n around the steady state\, and prove the algebraic decay in time of the F
ourier modes of their density. We prove moreover that these solutions exhi
bit a scattering behavior to a modified state\, implying a linear damping
effect with an algebraic rate of damping.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (University of Roma Tor Vergata)
DTSTART:20211013T140000Z
DTEND:20211013T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/18
DESCRIPTION:Title: Fast-slow partially hyperbolic Dynamical Systems\nby Carlang
elo Liverani (University of Roma Tor Vergata) as part of Dynamical systems
and PDEs\n\n\nAbstract\nFast-slow systems emerge naturally in many physic
al situations. While there exists a well-developed theory to investigate t
he statistical properties of strongly chaotic (uniformly hyperbolic) syste
ms\, little is known about fast-slow systems due to the presence of ``neut
ral directions” in which the dynamics does not mix very effectively. I w
ill describe some progress and obstacles of this research program.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences)
DTSTART:20211027T140000Z
DTEND:20211027T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/19
DESCRIPTION:Title: Mean-field limits for singular flows\nby Sylvia Serfaty (Cou
rant Institute of Mathematical Sciences) as part of Dynamical systems and
PDEs\n\n\nAbstract\nWe discuss the derivation of PDEs as limits as N tends
to infinity of the dynamics of N points for a certain class of Riesz-typ
e singular pair interactions. The method is based on studying the time evo
lution of a certain "modulated energy" and on proving a functional inequal
ity relating certain "commutators" to the modulated energy. When additive
noise is added\, in dimension at least 3 a uniform in time convergence can
even be obtained. Based on joint works with Hung Nguyen\, Matthew Rosenz
weig.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART:20211110T150000Z
DTEND:20211110T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/20
DESCRIPTION:Title: Small scale creation in active scalars\nby Alexander Kiselev
(Duke University) as part of Dynamical systems and PDEs\n\n\nAbstract\nAn
active scalar is advected by fluid velocity that is determined by the sca
lar itself. Active scalars appear in many situations in fluid mechanics\,
with the most classical example being 2D Euler equation in vorticity form.
Usually\, active scalar equations are both nonlinear and nonlocal\, and t
heir solutions spontaneously generate small scales. In this talk\, I will
discuss rigorous examples of small scale formation that involves infinite
in time growth of derivatives for the 2D Euler equation\, the SQG equation
and the 2D IPM equation.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Vakulenko (Institute of Problems in Mechanical Engineering\
, St. Petersbourg)
DTSTART:20211124T140000Z
DTEND:20211124T150000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/21
DESCRIPTION:Title: Universal dynamical approximation by Oberbeck-Boussinesque model
\nby Sergei Vakulenko (Institute of Problems in Mechanical Engineering
\, St. Petersbourg) as part of Dynamical systems and PDEs\n\n\nAbstract\nW
e consider dynamics defined by the Navier–Stokes equations in the Oberbe
ck–Boussinesq approximation in a two dimensional domain. This model of f
luid dynamics involves fundamental physical effects: convection and diffus
ion. The main result is as follows: local semiflows\, induced by this prob
lem\, can generate all possible structurally stable dynamics defined by C1
smooth vector fields on compact smooth manifolds (up to an orbital topolo
gical equivalence). To generate a prescribed dynamics\, it is sufficient t
o adjust some parameters in the equations\, namely\, the viscosity coeffic
ient\, an external heat source\, some parameters in boundary conditions an
d the small perturbation of the gravitational force.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tarek M Elgindi (Duke University)
DTSTART:20211215T150000Z
DTEND:20211215T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/22
DESCRIPTION:Title: Remarks on the long-time behavior of solutions of 2d Euler\n
by Tarek M Elgindi (Duke University) as part of Dynamical systems and PDEs
\n\n\nAbstract\nWe will discuss the basic results on the long-time behavio
r of solutions to the 2d Euler equation. Our focus will be on the loss of
regularity of solutions in infinite time. A well known problem is to estab
lish generic loss of regularity for solutions in the infinite time limit.
We will discuss some recent partial results in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armen Shirikyan (University of Cergy-Pontoise)
DTSTART:20220119T150000Z
DTEND:20220119T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/23
DESCRIPTION:Title: Global stabilisation of damped-driven conservation laws by a one
-dimensional forcing\nby Armen Shirikyan (University of Cergy-Pontoise
) as part of Dynamical systems and PDEs\n\n\nAbstract\nWe study a multidim
ensional conservation law in a bounded domain\, subject to a damping and a
n external force. Imposing the Dirichlet boundary condition and using stan
dard methods of parabolic PDEs\, it is straightforward to check that all t
he solutions are bounded in a Hölder space. Our main result proves that a
ny trajectory can be exponentially stabilised by a one-dimensional externa
l force supported in a given open subset. As a consequence\, we obtain the
global approximate controllability to trajectories by a one-dimensional
localised control. The proofs are based on the strong dissipation property
of the PDEs in question and the theory of positivity preserving semigroup
s.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (Instituto de Ciencias Matemáticas)
DTSTART:20220202T150000Z
DTEND:20220202T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/24
DESCRIPTION:Title: MHD equilibria in toroidal geometries\nby Daniel Peralta-Sal
as (Instituto de Ciencias Matemáticas) as part of Dynamical systems and P
DEs\n\n\nAbstract\nThe computation of 3D magnetohydrodynamics (MHD) equili
bria is of major importance for magnetic confinement devices such as tokam
aks or stellarators. In this talk I will present recent results on the exi
stence of stepped pressure MHD equilibria in 3D toroidal domains\, where t
he plasma current exhibits an arbitrary number of current sheets. The toro
idal domains where these equilibria are shown to exist do not need to be s
mall perturbations of an axisymmetric domain\, and in fact they can have a
ny knotted topology. The proof involves three main ingredients: a Cauchy-K
ovalevskaya theorem for Beltrami fields\, a Hamilton-Jacobi equation on th
e two-dimensional torus\, and a KAM theorem for divergence-free fields in
three dimensions. This is based on joint work with A. Enciso and A. Luque.
\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Kuksin (University Paris 7 Diderot)
DTSTART:20220216T150000Z
DTEND:20220216T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/25
DESCRIPTION:Title: Two models for wave turbulence\nby Sergei Kuksin (University
Paris 7 Diderot) as part of Dynamical systems and PDEs\n\n\nAbstract\nI w
ill talk on the recent progress in rigorous justifying a deterministic and
a stochastic models for wave turbulence\, mostly concentrating on the lat
ter.\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough University)
DTSTART:20220302T150000Z
DTEND:20220302T160000Z
DTSTAMP:20260404T111245Z
UID:DSandPDEs/26
DESCRIPTION:Title: Symplectic invariants of integrable Hamiltonian systems\nby
Alexey Bolsinov (Loughborough University) as part of Dynamical systems and
PDEs\n\n\nAbstract\nTwo integrable systems are called symplectically equi
valent\, if there exists a symplectic diffeomorphism between the correspon
ding phase spaces that sends Liouville tori of one system to those of the
other. This review talk will be devoted to symplectic invariants of integ
rable systems\, i.e. those which allow us to decide whether or not two giv
en systems are symplectically equivalent. My goal will be to explain that
in many cases such invariants can be reconstructed from action variables.
\n
LOCATION:https://stable.researchseminars.org/talk/DSandPDEs/26/
END:VEVENT
END:VCALENDAR