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BEGIN:VEVENT
SUMMARY:Sergei KUKSIN (University Paris 7 Diderot)
DTSTART;VALUE=DATE-TIME:20200930T140000Z
DTEND;VALUE=DATE-TIME:20200930T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/1
DESCRIPTION:Title: Kolmogorov theory of turbulence and its rigorous model\, given by the Bu
rgers equation\nby Sergei KUKSIN (University Paris 7 Diderot) as part
of Dynamical systems and PDEs\n\n\nAbstract\nI will present three main law
s from the Kolmogorov theory of turbulence ("the K41 model")\, discuss the
ir versions for one-dimensional fluid and will show that the latter may be
rigorously justified for the 1d fluid\, described by the Burgers equation
\, via a qualitative analysis of the dynamical system which the equation d
efines in Sobolev spaces. The talk is based on a MS of my joint book with
Alex Boritchev.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela PROCESI (Università degli Studi Roma Tre)
DTSTART;VALUE=DATE-TIME:20201014T140000Z
DTEND;VALUE=DATE-TIME:20201014T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
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 periodic
solutions for evolution PDEs is a very interesting problem\, with a lot o
f open questions. Most of the literature is on the construction of very re
gular solutions for semilinear PDEs (mainly the NLS) with external paramet
ers. I shall discuss two new results: 1. existence of solutions for a quas
i-linear forced Airy equation\, 2. existence of finite regularity solution
s for the traslation invariant NLS equation.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei TABACHNIKOV (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20201028T150000Z
DTEND;VALUE=DATE-TIME:20201028T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/3
DESCRIPTION:Title: Flavors of bicycle mathematics\nby Sergei TABACHNIKOV (Pennsylvania
State University) as part of Dynamical systems and PDEs\n\n\nAbstract\nThi
s talk concerns a naive model of bicycle motion: a bicycle is a segment 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 quite rich
and has connections with several areas of research\, including completely
integrable systems. Here is a sampler of problems that I hope to touch upo
n:\n1) The trajectory of the front wheel and the initial position of the b
icycle uniquely determine its motion and its terminal position\; the monod
romy map sending the initial position to the terminal one arises. This map
ping is a Moebius transformation\, a remarkable fact that has various geom
etrical and dynamical consequences.\n2) The rear wheel track and a choice
of the direction of motion uniquely determine the front wheel track\; chan
ging the direction to the opposite\, yields another front track. These two
front tracks are related by the bicycle (Backlund\, Darboux) corresponden
ce\, which defines a discrete time dynamical system on the space of curves
. This system is completely integrable and it is closely related with anot
her\, well studied\, completely integrable dynamical system\, the filament
(a.k.a binormal\, smoke ring\, local induction) equation.\n3) Given the r
ear and front tracks of a bicycle\, can one tell which way the bicycle wen
t? 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 the only
body that floats in equilibrium in all positions? This problem is also re
lated to the motion of a charge in a magnetic field of a special kind. It
turns out that the known solutions are solitons of the planar version of t
he filament equation.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Denisov (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20201125T150000Z
DTEND;VALUE=DATE-TIME:20201125T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/4
DESCRIPTION:Title: Singularity formation in the contour dynamics for 2d Euler equation on t
he plane\nby Sergey Denisov (University of Wisconsin-Madison) as part
of Dynamical systems and PDEs\n\n\nAbstract\nWe will study 2d Euler dynami
cs of centrally symmetric pair of patches on the plane. In the presence of
exterior regular velocity\, we will show that these patches can merge 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 discuss
ed. For a model equation\, we will discuss existence of the curve of smoot
h stationary solutions that originates at singular stationary steady state
.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Niederman (University Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20201209T150000Z
DTEND;VALUE=DATE-TIME:20201209T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/5
DESCRIPTION:Title: Quasi periodic co-orbital motions (joint work with Philippe Robutel and
Alexandre Pousse)\nby Laurent Niederman (University Paris-Saclay) as
part of Dynamical systems and PDEs\n\n\nAbstract\nThe motions of the satel
lites Janus and Epimetheus around Saturn are among the most intriguing 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 orbits (
hence stable) which exhibit this exchange property in the three body plane
planetary problem thanks to KAM theory.\n\n[1] On the Co-orbital Motion i
n the Three-Body Problem: Existence of Quasi-periodic Horseshoe-Shaped Orb
its\, L. Niederman\, A. Pousse\, P. Robutel\, Comm. Math. Phys.\, vol. 377
\, pp. 551–612 (2020)\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Polterovich (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20201223T150000Z
DTEND;VALUE=DATE-TIME:20201223T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/6
DESCRIPTION:Title: Instabilities in Hamiltonian dynamics and symplectic topology\nby Le
onid Polterovich (Tel Aviv University) as part of Dynamical systems and PD
Es\n\n\nAbstract\nI outline an existence mechanism\, based on symplectic t
opology\, for orbits of Hamiltonian flows connecting a pair of disjoint su
bsets in the phase space. Applications include "superconductivity channels
" in nearly integrable systems\, and contact dynamics (joint with Michael
Entov).\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabelle Gallagher (École Normale Supérieure)
DTSTART;VALUE=DATE-TIME:20210127T150000Z
DTEND;VALUE=DATE-TIME:20210127T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/7
DESCRIPTION:Title: On the derivation of the Boltzmann equation: fluctuations and large devi
ations\nby Isabelle Gallagher (École Normale Supérieure) as part of
Dynamical systems and PDEs\n\n\nAbstract\nIt has been known since Lanford
’s result in 1974 that in the limit when the number of particles goes to
infinity in a rarefied gas\, the one-particle distribution satisfies the
Boltzmann equation\, at least for a short time. In this talk we shall anal
yze the fluctuations\, and large deviations around that limit. This corres
ponds to joint works with Thierry Bodineau\, Laure Saint-Raymond and Sergi
o Simonella.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Novikov (École Polytechnique\, France & IEPT RAS\, Russia)
DTSTART;VALUE=DATE-TIME:20210210T150000Z
DTEND;VALUE=DATE-TIME:20210210T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/8
DESCRIPTION:Title: Multidimensional inverse scattering problem for the Schrödinger equatio
n\nby Roman Novikov (École Polytechnique\, France & IEPT RAS\, Russi
a) as part of Dynamical systems and PDEs\n\n\nAbstract\nWe give a short re
view of old and recent results on the multidimensional inverse scattering
problem for the Schrödinger equation.\nA special attention is paid to eff
icient reconstructions of the potential from scattering data which can be
measured in practice.\nPotential applications include phaseless inverse X-
ray scattering\, acoustic tomography and tomographies using elementary par
ticles.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Kleptsyn (Institute of Mathematical Research of Rennes)
DTSTART;VALUE=DATE-TIME:20210224T150000Z
DTEND;VALUE=DATE-TIME:20210224T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/9
DESCRIPTION:Title: The Furstenberg theorem : adding a parameter and removing the stationari
ty (on a joint work with A. Gorodetski)\nby Victor Kleptsyn (Institute
of Mathematical Research of Rennes) as part of Dynamical systems and PDEs
\n\n\nAbstract\nThe classical Furstenberg theorem describes the (almost su
re) 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 w
hat happens if the random matrices from SL(2\,R) depend on an additional p
arameter. It turns out that in this new situation\, the conclusion changes
. Namely\, under some natural conditions\, there almost surely exists a (r
andom) "exceptional" set on parameters where the lower limit for the Lyapu
nov exponent vanishes.\nAnother direction of the generalization of the cla
ssical Furstenberg theorem is removing the stationarity assumption. That i
s\, the matrices that are multiplied are still independent\, but no longer
identically distributed. Though in this setting most of the standard tool
s are no longer applicable (no more stationary measure\, no more Birkhoff
ergodic theorem\, etc.)\, it turns out that the Furstenberg theorem can (u
nder the appropriate assumptions) still be generalized to this setting\, w
ith a deterministic sequence replacing the Lyapunov exponent. These two ge
neralizations can be mixed together\, providing the Anderson localization
conclusions for the non-stationary 1D random Schrodinger operators.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Stolovitch (University of Côte d'Azur)
DTSTART;VALUE=DATE-TIME:20210310T150000Z
DTEND;VALUE=DATE-TIME:20210310T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/10
DESCRIPTION:Title: Geometry of hyperbolic Cauchy-Riemann singularities and KAM-like theory
for holomorphic involutions\nby Laurent Stolovitch (University of Cô
te d'Azur) as part of Dynamical systems and PDEs\n\n\nAbstract\nIn this ta
lk\, we emphasize how the understanding of the properties of some dynamica
l systems can lead to the understandings of some (a priori unrelated) geom
etric problems.\n\nTo be more specific\, we shall give some new insights o
f the geometry of germs of real analytic surfaces in (C^2\,0) having an is
olated Cauchy-Riemann (CR) singularity at the origin. These are perturbati
ons of Bishop quadrics. There are two kinds of CR singularities stable und
er perturbations: elliptic and hyperbolic. Elliptic case was studied by Mo
ser-Webster in their seminal '83 article\, where they showed that such a s
urface is locally\, near the CR singularity\, holomorphically equivalent t
o normal form from which lots of geometric/analytic features can be read o
ff.\n\nHere\, we focus on perturbations of hyperbolic quadrics. As was sho
wn 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 surfac
e M in (C^2\,0) having a hyperbolic CR singularity at the origin\, we pro
ve the existence of Whitney smooth family of holomorphic curves intersecti
ng M along holomorphic hyperbolas. This is the very first result concernin
g hyperbolic CR singularity not equivalent to quadrics.\n \n This is a c
onsequence of a non-standard KAM-like theorem for pair of germs of holomor
phic involutions $\\{\\tau_1\,\\tau_2\\}$ at the origin\, a common fixed p
oint. We show that such a pair has large amount of invariant analytic sets
biholomorphic to $\\{z_1z_2=const\\}$ (which is not the usual torus) in a
neighborhood of the origin\, and that they are conjugate to restrictions
of linear maps on such invariant sets. This is a joint work with Z. Zhao.\
n
LOCATION:https://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;VALUE=DATE-TIME:20210324T150000Z
DTEND;VALUE=DATE-TIME:20210324T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/11
DESCRIPTION:Title: Geodesic scattering on hyperboloids and Knoerrer’s map\nby Alexan
der Veselov (Loughborough University\, UK\; Moscow State University and St
eklov Mathematical Institute\, Russia) as part of Dynamical systems and PD
Es\n\n\nAbstract\nGeodesic flow on ellipsoids is one of the most celebrate
d classical integrable systems considered by Jacobi in 1837. Moser revisit
ed this problem in 1978 revealing the link with the modern theory of solit
ons. Surprisingly a similar question for hyperboloids did not get much att
ention\, although the dynamics in this case is very different.\n\nI will e
xplain how to use the remarkable results of Moser and Knoerrer on the rela
tions between Jacobi problem and integrable Neumann system on sphere to de
scribe explicitly the geodesic scattering on hyperboloids. It will be show
n also that Knoerrer's reparametrisation is closely related to the project
ively equivalent metric on a quadric discovered in 1998 by Tabachnikov and
\, independently\, by Matveev and Topalov\, giving a new proof of their re
sult. The projectively equivalent metric (in contrast to the usual one) tu
rns out to be regular on the projective closure of hyperboloid\, which all
ows us to extend Knoerrer's map to this closure. \n\nThe talk is based on
a recent joint work with Lihua Wu.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wilhelm Schlag (Yale University)
DTSTART;VALUE=DATE-TIME:20210407T140000Z
DTEND;VALUE=DATE-TIME:20210407T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/12
DESCRIPTION:Title: On the long-term dynamics of nonlinear wave equations and the uniquenes
s of solitons\nby Wilhelm Schlag (Yale University) as part of Dynamica
l systems and PDEs\n\n\nAbstract\nWe will discuss the problem of existence
and uniqueness of nonzero solutions of finite energy to semilinear ellipt
ic PDEs. The uniqueness question\, which is often delicate\, has consequen
ces for the spectral properties of the linearized operators. This in turn
is of essence for the long-term dynamics of solutions. In particular\, I w
ill describe recent work with Alex Cohen and Kevin Li at Yale on the long-
standing problem of uniqueness of the first few excited states for the cub
ic problem in three dimensions.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francois Huveneers (University Paris-Dauphine)
DTSTART;VALUE=DATE-TIME:20210421T140000Z
DTEND;VALUE=DATE-TIME:20210421T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/13
DESCRIPTION:Title: Integrability breaking in extended Hamiltonian systems\nby Francois
Huveneers (University Paris-Dauphine) as part of Dynamical systems and PD
Es\n\n\nAbstract\nIn low dimensional Hamiltonian systems\, several classic
al results such as the KAM theorem or Nekhoroshev estimates guarantee that
the dynamics remains close to integrable in the vicinity of an integrable
point. In statistical physics and thermodynamics\, one needs to consider
extensive systems at positive temperature. In this case\, the common belie
f is that integrability is completely lost as soon as one leaves the integ
rable limit. Nevertheless\, as we will see in this talk\, the dynamics on
some intermediate time scales may be strongly affected by integrable effec
ts. The understanding of the dynamics on such timescales is directly relev
ant to evaluate the thermal or electrical conductivity.\n\nThe talk will c
onsist of two parts: First\, I will introduce the topic\, describe the phe
nomenology and state a few mathematical results that we obtained in the la
st years (works with W. De Roeck). Second\, I will discuss the Green-Kubo
formula for the conductivity and I will present some open problems related
to our results.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dario Bambusi (University of Milan)
DTSTART;VALUE=DATE-TIME:20210512T140000Z
DTEND;VALUE=DATE-TIME:20210512T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/14
DESCRIPTION:Title: Growth of Sobolev norms for unbounded perturbations of the Laplacian on
flat tori (towards a quantum Nekhoroshev theorem)\nby Dario Bambusi
(University of Milan) as part of Dynamical systems and PDEs\n\n\nAbstract\
nI will present a study of the time dependent Schr\\"odinger\nequation\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\npseudodifferent
ial operator of order strictly smaller than 2. The main result I will give
is an estimate\nensuring that the Sobolev norms of the solutions are boun
ded by\n$t^{\\epsilon}$. The proof is a quantization of the proof of the\n
Nekhoroshev theorem\, both analytic and geometric parts.\n\nPrevious resul
ts of this kind were limited either to the case of\nbounded perturbations
of the Laplacian or to quantization of systems\nwith a trivial geometry of
the resonances\, lik harmonic oscillators or\n1-d systems. \n\nIn this se
minar 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://researchseminars.org/talk/DSandPDEs/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bedrossian (University of Maryland)
DTSTART;VALUE=DATE-TIME:20210526T140000Z
DTEND;VALUE=DATE-TIME:20210526T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/15
DESCRIPTION:Title: A regularity method for lower bounds on the Lyapunov exponent for stoch
astic differential equations\nby Jacob Bedrossian (University of Maryl
and) as part of Dynamical systems and PDEs\n\n\nAbstract\nIn a recent join
t work with Alex Blumenthal and Sam Punshon-Smith\, we put forward a new m
ethod for obtaining quantitative lower bounds on the top Lyapunov exponent
of stochastic differential equations (SDEs). Our method combines (i) an (
apparently new) identity connecting the top Lyapunov exponent to a degener
ate Fisher information-like functional of the stationary density of the Ma
rkov process tracking tangent directions with (ii) a quantitative version
of Hörmander’s hypoelliptic regularity theory in an L1 framework which
estimates this Fisher information from below by a fractional Sobolev norm
using the Kolmogorov equation.. As an initial application\, we prove the p
ositivity of the top Lyapunov exponent for a class of weakly-dissipative\,
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-dimensional trunc
ations of shell models GOY and SABRA). This is the first mathematically ri
gorous proof of chaos (in the sense of positive Lyapunov exponents) for st
ochastically driven Lorenz 96\, despite the overwhelming numerical evidenc
e (the deterministic case remains far out of reach).\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Mironov (Sobolev Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20210609T140000Z
DTEND;VALUE=DATE-TIME:20210609T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/16
DESCRIPTION:Title: Commuting differential and difference operators\nby Andrey Mironov
(Sobolev Institute of Mathematics) as part of Dynamical systems and PDEs\n
\n\nAbstract\nWe will discuss the connection between commuting ordinary di
fferential operators and commuting difference operators. In particular\, w
e construct a discretization of the Lamé operator that preserves the spec
tral curve.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erwan Faou (INRIA-Rennes & IRMAR University of Rennes)
DTSTART;VALUE=DATE-TIME:20210929T140000Z
DTEND;VALUE=DATE-TIME:20210929T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/17
DESCRIPTION:Title: Linear damping around inhomogeneous stationary states of the Vlasov-HMF
model\nby Erwan Faou (INRIA-Rennes & IRMAR University of Rennes) as p
art of Dynamical systems and PDEs\n\n\nAbstract\nWe will consider the dyna
mics of perturbations around an inhomogeneous stationary state of the Vlas
ov-HMF (Hamiltonian Mean-Field) model\, satisfying a linearized stability
criterion. Such stationary states are closely related to the dynamics of t
he pendulum system. We consider solutions of the linearized equation aroun
d the steady state\, and prove the algebraic decay in time of the Fourier
modes of their density. We prove moreover that these solutions exhibit a s
cattering behavior to a modified state\, implying a linear damping effect
with an algebraic rate of damping.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlangelo Liverani (University of Roma Tor Vergata)
DTSTART;VALUE=DATE-TIME:20211013T140000Z
DTEND;VALUE=DATE-TIME:20211013T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/18
DESCRIPTION:Title: Fast-slow partially hyperbolic Dynamical Systems\nby Carlangelo Liv
erani (University of Roma Tor Vergata) as part of Dynamical systems and PD
Es\n\n\nAbstract\nFast-slow systems emerge naturally in many physical situ
ations. While there exists a well-developed theory to investigate the stat
istical properties of strongly chaotic (uniformly hyperbolic) systems\, li
ttle is known about fast-slow systems due to the presence of ``neutral dir
ections” in which the dynamics does not mix very effectively. I will des
cribe some progress and obstacles of this research program.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvia Serfaty (Courant Institute of Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20211027T140000Z
DTEND;VALUE=DATE-TIME:20211027T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/19
DESCRIPTION:Title: Mean-field limits for singular flows\nby Sylvia Serfaty (Courant In
stitute 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 inf
inity of the dynamics of N points for a certain class of Riesz-type singu
lar pair interactions. The method is based on studying the time evolution
of a certain "modulated energy" and on proving a functional inequality rel
ating certain "commutators" to the modulated energy. When additive noise i
s added\, in dimension at least 3 a uniform in time convergence can even b
e obtained. Based on joint works with Hung Nguyen\, Matthew Rosenzweig.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kiselev (Duke University)
DTSTART;VALUE=DATE-TIME:20211110T150000Z
DTEND;VALUE=DATE-TIME:20211110T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
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 scalar its
elf. Active scalars appear in many situations in fluid mechanics\, with th
e most classical example being 2D Euler equation in vorticity form. Usuall
y\, active scalar equations are both nonlinear and nonlocal\, and their so
lutions 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 th
e 2D IPM equation.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Vakulenko (Institute of Problems in Mechanical Engineering\
, St. Petersbourg)
DTSTART;VALUE=DATE-TIME:20211124T140000Z
DTEND;VALUE=DATE-TIME:20211124T150000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/21
DESCRIPTION:Title: Universal dynamical approximation by Oberbeck-Boussinesque model\nb
y Sergei Vakulenko (Institute of Problems in Mechanical Engineering\, St.
Petersbourg) as part of Dynamical systems and PDEs\n\n\nAbstract\nWe consi
der dynamics defined by the Navier–Stokes equations in the Oberbeck–Bo
ussinesq approximation in a two dimensional domain. This model of fluid dy
namics involves fundamental physical effects: convection and diffusion. Th
e main result is as follows: local semiflows\, induced by this problem\, c
an generate all possible structurally stable dynamics defined by C1 smooth
vector fields on compact smooth manifolds (up to an orbital topological e
quivalence). To generate a prescribed dynamics\, it is sufficient to adjus
t some parameters in the equations\, namely\, the viscosity coefficient\,
an external heat source\, some parameters in boundary conditions and the s
mall perturbation of the gravitational force.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tarek M Elgindi (Duke University)
DTSTART;VALUE=DATE-TIME:20211215T150000Z
DTEND;VALUE=DATE-TIME:20211215T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/22
DESCRIPTION:Title: Remarks on the long-time behavior of solutions of 2d Euler\nby Tare
k M Elgindi (Duke University) as part of Dynamical systems and PDEs\n\n\nA
bstract\nWe will discuss the basic results on the long-time behavior of so
lutions to the 2d Euler equation. Our focus will be on the loss of regular
ity of solutions in infinite time. A well known problem is to establish ge
neric loss of regularity for solutions in the infinite time limit. We will
discuss some recent partial results in this direction.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Armen Shirikyan (University of Cergy-Pontoise)
DTSTART;VALUE=DATE-TIME:20220119T150000Z
DTEND;VALUE=DATE-TIME:20220119T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/23
DESCRIPTION:Title: Global stabilisation of damped-driven conservation laws by a one-dimens
ional forcing\nby Armen Shirikyan (University of Cergy-Pontoise) as pa
rt of Dynamical systems and PDEs\n\n\nAbstract\nWe study a multidimensiona
l conservation law in a bounded domain\, subject to a damping and an exter
nal force. Imposing the Dirichlet boundary condition and using standard me
thods of parabolic PDEs\, it is straightforward to check that all the solu
tions are bounded in a Hölder space. Our main result proves that any traj
ectory can be exponentially stabilised by a one-dimensional external force
supported in a given open subset. As a consequence\, we obtain the globa
l approximate controllability to trajectories by a one-dimensional localis
ed control. The proofs are based on the strong dissipation property of the
PDEs in question and the theory of positivity preserving semigroups.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Peralta-Salas (Instituto de Ciencias Matemáticas)
DTSTART;VALUE=DATE-TIME:20220202T150000Z
DTEND;VALUE=DATE-TIME:20220202T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
UID:DSandPDEs/24
DESCRIPTION:Title: MHD equilibria in toroidal geometries\nby Daniel Peralta-Salas (Ins
tituto de Ciencias Matemáticas) as part of Dynamical systems and PDEs\n\n
\nAbstract\nThe computation of 3D magnetohydrodynamics (MHD) equilibria is
of major importance for magnetic confinement devices such as tokamaks or
stellarators. In this talk I will present recent results on the existence
of stepped pressure MHD equilibria in 3D toroidal domains\, where the plas
ma current exhibits an arbitrary number of current sheets. The toroidal do
mains where these equilibria are shown to exist do not need to be small pe
rturbations of an axisymmetric domain\, and in fact they can have any knot
ted topology. The proof involves three main ingredients: a Cauchy-Kovalevs
kaya theorem for Beltrami fields\, a Hamilton-Jacobi equation on the two-d
imensional torus\, and a KAM theorem for divergence-free fields in three d
imensions. This is based on joint work with A. Enciso and A. Luque.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Kuksin (University Paris 7 Diderot)
DTSTART;VALUE=DATE-TIME:20220216T150000Z
DTEND;VALUE=DATE-TIME:20220216T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
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 will tal
k on the recent progress in rigorous justifying a deterministic and a stoc
hastic models for wave turbulence\, mostly concentrating on the latter.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough University)
DTSTART;VALUE=DATE-TIME:20220302T150000Z
DTEND;VALUE=DATE-TIME:20220302T160000Z
DTSTAMP;VALUE=DATE-TIME:20240329T072919Z
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 equivalent\
, if there exists a symplectic diffeomorphism between the corresponding ph
ase spaces that sends Liouville tori of one system to those of the other.
This review talk will be devoted to symplectic invariants of integrable s
ystems\, i.e. those which allow us to decide whether or not two given syst
ems are symplectically equivalent. My goal will be to explain that in man
y cases such invariants can be reconstructed from action variables.\n
LOCATION:https://researchseminars.org/talk/DSandPDEs/26/
END:VEVENT
END:VCALENDAR