Remarks on Landau damping

Abstract

We provide few remarks on nonlinear Landau damping that concerns decay of the electric field in the classical Vlasov-Poisson system near spatially homogenous equilibria. In particular, this includes the analyticity framework, \`a la Grenier-Nguyen-Rodnianski, for non specialists, treating the analytic case studied by Mouhot-Villani, among other remarks for plasmas confined on a torus and in the whole space. Finally, we also establish the nonlinear Landau damping for a family of Vlasov-Riesz systems, which are new and surprisingly include the borderline Vlasov-Dirac-Benney system in the sharp analytic spaces.