# Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates

## TL;DR

This paper provides a new proof of Landau damping for screened Vlasov-Poisson systems using a Lagrangian approach and pointwise dispersive estimates, reducing initial data smoothness requirements and achieving sharp decay rates.

## Contribution

It introduces a Lagrangian-based proof with pointwise dispersive estimates for the linearized problem, lowering smoothness assumptions and matching free transport decay rates.

## Key findings

- Reduced initial data regularity to Lipschitz
- Established sharp time decay estimates
- Extended Landau damping proof to screened interactions

## Abstract

We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov-Poisson systems with screened interactions in the whole space $\mathbb{R}^d$ (for $d\geq3$) that was first established by Bedrossian, Masmoudi and Mouhot. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in Bedrossian at al. (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.