|DATE||February 15 (Mon), 2021|
|INSTITUTE||ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE|
|TITLE||On asymptotic stability in the Vlasov-Poisson system|
|ABSTRACT|| In this talk we discuss some recent work on the asymptotic stability of two classic equilibria of the Vlasov-Poisson system: vacuum and a point charge. Starting with an overview of the classic theory in these settings (which guarantees the global existence of smooth solutions under suitable conditions on the initial data) we introduce a new approach that combines a Lagrangian analysis of the linearized problem with an Eulerian PDE framework in the nonlinear analysis, all the while respecting the symplectic structure. For sufficiently small data, in both of the above cases the asymptotic behavior is then seen to be a modified scattering dynamic, which we can precisely quantify.
This is joint work with Benoit Pausader (Brown University).