Landau damping on the torus for the Vlasov-Poisson system with massless electrons

TL;DR

This paper proves exponential decay of solutions in the Vlasov-Poisson system with massless electrons on the torus, extending Landau damping results to more general nonlinear couplings and ion models.

Contribution

It extends Landau damping analysis to the Vlasov-Poisson system with massless electrons on the torus, including analytic and Gevrey initial data, and broadens applicability to nonlinear couplings.

Findings

Exponential decay of density and force fields for solutions near equilibrium.

Extension of Landau damping results to systems with ions and nonlinear couplings.

Decay results hold for analytic or Gevrey initial data with $ ext{Gevrey} > 1/3$.

Abstract

This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$ for the Vlasov-Poisson system with massless electrons (VPME). We consider solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a homogeneous equilibrium satisfying a Penrose stability condition. We show that for such solutions, the corresponding density and force field decay exponentially fast as time goes to infinity. This work extends the results for Vlasov-Poisson on the torus to the case of ions and, more generally, to arbitrary analytic nonlinear couplings.