Séminaires : Dynamical systems and PDEs

Equipe(s) : gd,
Responsables :Sergei Kuksin, Dmitrii Treschev
Email des responsables : sergei.kuksin@imj-prg.fr
Salle : https://mi-ras-ru.zoom.us/j/98541889798?pwd=SGdnT2lPWCtrbzNjOHQyb09NS0dXdz09
Adresse :Zoom
Description Paris 7 Diderot & Steklov Mathematical Institute Online Seminar

Orateur(s) Faou - INRIA-Rennes & IRMAR University of Rennes,
Titre Linear damping around inhomogeneous stationary states of the Vlasov-HMF model
Horaire16:00 à 17:00
RésumeWe will consider the dynamics of perturbations around an inhomogeneous stationary state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion. Such stationary states are closely related to the dynamics of the pendulum system. We consider solutions of the linearized equation around 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 scattering behavior to a modified state, implying a linear damping effect with an algebraic rate of damping.