The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric

TL;DR

This paper investigates the quasineutral limit of the 1D Vlasov-Poisson equation, providing new stability estimates in Wasserstein metric that extend convergence results without requiring uniform analytic regularity.

Contribution

It introduces novel weak-strong stability estimates in Wasserstein metric, enabling convergence analysis for less regular initial data in the quasineutral limit.

Findings

Established new stability estimates in Wasserstein metric

Extended convergence results to less regular initial data

Proved the formal limit holds under broader conditions

Abstract

In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation for ions with massless thermalized electrons. We prove new weak-strong stability estimates in the Wasserstein metric that allow us to extend and improve previously known convergence results. In particular, we show that given a possibly unstable analytic initial profile, the formal limit holds for sequences of measure initial data converging sufficiently fast in the Wasserstein metric to this profile. This is achieved without assuming uniform analytic regularity.