On the linearized Vlasov-Poisson system on the whole space around stable homogeneous equilibria

TL;DR

This paper analyzes the linearized Vlasov-Poisson system around stable equilibria in any dimension, establishing dispersive decay estimates in the physical space, which enhances understanding of plasma stability and wave dispersion.

Contribution

It provides the first dispersive $L^ Infty$ decay estimates for the linearized Vlasov-Poisson system on the whole space in arbitrary dimensions.

Findings

Dispersive decay estimates are established for the linearized system.

Results hold for any spatial dimension $d \\geq 1$.

The work advances the mathematical understanding of plasma stability.

Abstract

We study the linearized Vlasov-Poisson system around suitably stable homogeneous equilibria on $\mathbb{R}^d\times \mathbb{R}^d$ (for any $d \geq 1$) and establish dispersive $L^\infty$ decay estimates in the physical space.