On the stability of vacuum in the screened Vlasov-Poisson equation

Abstract

We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on ${\mathbb{R}}^d\times {\mathbb{R}}^d$ near vacuum. We show that for dimensions $d\ge 2$, under mild assumptions on localization (in terms of spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions scatter freely. In dimension $d=1$, we obtain a long time existence result in analytic regularity.

30 pages; final version as accepted for publication