Landau Damping in a weakly collisional regime

TL;DR

This paper demonstrates that Landau damping persists in the nonlinear Vlasov-Poisson equations even when a weak collisional effect is introduced via the linear Boltzmann collision operator.

Contribution

It extends the understanding of Landau damping to weakly collisional regimes within the nonlinear Vlasov-Poisson framework.

Findings

Landau damping occurs in the weakly collisional regime.

The linear Boltzmann collision operator does not prevent damping.

Damping persists despite the presence of collisions.

Abstract

In this paper, we consider the nonlinear Vlasov-Poisson equations in a weakly collisional regime and study the linear Boltzmann collision operator. We prove that Landau damping still occurs in this case.