On the local uniqueness of steady states for the Vlasov-Poisson system

TL;DR

This paper investigates the local uniqueness of steady states in the Vlasov-Poisson system, building on recent stability results and drawing parallels with 2D Euler equations to deepen understanding of plasma and galactic dynamics.

Contribution

It provides new insights into the local uniqueness of steady states for the Vlasov-Poisson system, extending stability analysis methods from fluid dynamics to plasma physics.

Findings

Establishes conditions for local uniqueness of steady states

Connects stability results with uniqueness properties

Provides a framework for analyzing steady states near known solutions

Abstract

Motivated by recent results of Lemou-M\'ehats-R\"aphael and Lemou concerning the quatitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these one. This research is inspired by analogous results of Couffrut and \v{S}ver\'ak in the context of the 2D Euler equations.