Formation of small scales in nonlinear PDEs

Landau damping for screened Vlasov-Poisson on the whole space

Toan Nguyen

Penn State University

After a quick review on the problem, I shall present an alternative proof of the Landau damping on the whole space, which was first established by Bedrossian, Masmoudi and Mouhot. The proof follows a Lagrangian approach and relies on the derivation of precise pointwise in time dispersive estimates in the physical space for the linearized problem. In particular, this allows to cut down the smoothness of the initial data (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction. This is a joint work with Daniel Han-Kwan (Ecole polytechnique) and Frederic Rousset (Paris-Sud University).