Nonlinear stability of the one dimensional screened Vlasov Poisson equation

Abstract

We study the asymptotic behavior of small data solutions to the screened Vlasov Poisson(i.e. Vlasov-Yukawa) equation on $\mathbb{R}\times \mathbb{R}$ near vacuum. We show that for initial data small in Gevrey-2 regularity, the derivative of the density of order $n$ decays like $(t+1{)}^{-n-1}$.

18 pages