Nonlinear stability of the one dimensional screened Vlasov Poisson equation

TL;DR

This paper investigates the long-term behavior of small solutions to the one-dimensional screened Vlasov-Poisson equation, demonstrating decay rates of the density derivatives for initial data with Gevrey-2 regularity.

Contribution

It establishes nonlinear stability and decay estimates for solutions near vacuum in the one-dimensional screened Vlasov-Poisson system with Gevrey-2 initial data.

Findings

Density derivatives decay like (t+1)^{-n-1} for small initial data.

Solutions exhibit nonlinear stability near vacuum.

Decay rates depend on the order of derivatives.

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 $(t+1)^{-n-1}$.