BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergei KUKSIN (University Paris 7 Diderot) DTSTART:20200930T140000Z DTEND:20200930T150000Z DTSTAMP:20260422T225929Z 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:20201014T140000Z DTEND:20201014T150000Z DTSTAMP:20260422T225929Z 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:20201028T150000Z DTEND:20201028T160000Z DTSTAMP:20260422T225929Z 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:20201125T150000Z DTEND:20201125T160000Z DTSTAMP:20260422T225929Z 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:20201209T150000Z DTEND:20201209T160000Z DTSTAMP:20260422T225929Z 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:20201223T150000Z DTEND:20201223T160000Z DTSTAMP:20260422T225929Z 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:20210127T150000Z DTEND:20210127T160000Z DTSTAMP:20260422T225929Z 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:20210210T150000Z DTEND:20210210T160000Z DTSTAMP:20260422T225929Z 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:20210224T150000Z DTEND:20210224T160000Z DTSTAMP:20260422T225929Z 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:20210310T150000Z DTEND:20210310T160000Z DTSTAMP:20260422T225929Z 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:20210324T150000Z DTEND:20210324T160000Z DTSTAMP:20260422T225929Z 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:20210407T140000Z DTEND:20210407T150000Z DTSTAMP:20260422T225929Z 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:20210421T140000Z DTEND:20210421T160000Z DTSTAMP:20260422T225929Z 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:20210512T140000Z DTEND:20210512T150000Z DTSTAMP:20260422T225929Z 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:20210526T140000Z DTEND:20210526T150000Z DTSTAMP:20260422T225929Z 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:20210609T140000Z DTEND:20210609T150000Z DTSTAMP:20260422T225929Z 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:20210929T140000Z DTEND:20210929T150000Z DTSTAMP:20260422T225929Z 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:20211013T140000Z DTEND:20211013T150000Z DTSTAMP:20260422T225929Z 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:20211027T140000Z DTEND:20211027T150000Z DTSTAMP:20260422T225929Z 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:20211110T150000Z DTEND:20211110T160000Z DTSTAMP:20260422T225929Z 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:20211124T140000Z DTEND:20211124T150000Z DTSTAMP:20260422T225929Z 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:20211215T150000Z DTEND:20211215T160000Z DTSTAMP:20260422T225929Z 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:20220119T150000Z DTEND:20220119T160000Z DTSTAMP:20260422T225929Z 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:20220202T150000Z DTEND:20220202T160000Z DTSTAMP:20260422T225929Z 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:20220216T150000Z DTEND:20220216T160000Z DTSTAMP:20260422T225929Z 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:20220302T150000Z DTEND:20220302T160000Z DTSTAMP:20260422T225929Z 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