Nonlinear Landau damping and wave operators in sharp Gevrey spaces

TL;DR

This paper establishes nonlinear Landau damping and constructs scattering operators in optimal weighted Gevrey-3 spaces for the confined Vlasov-Poisson system, resolving two major open problems in the field.

Contribution

It proves nonlinear Landau damping in optimal Gevrey spaces and constructs associated scattering operators with injectivity and Lipschitz properties.

Findings

Proves nonlinear Landau damping in weighted Gevrey-3 spaces.

Constructs nonlinear scattering operators with stability properties.

Provides solutions to two open problems in plasma physics theory.

Abstract

We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the existence of nonlinear scattering operators associated to the confined Vlasov-Poisson evolution, as well as suitable injectivity properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these operators. Our results give definitive answers to two well-known open problems in the field, both of them stated in the recent review of Bedrossian [4, Section 6].