Quasineutral limit for Vlasov-Poisson with Penrose stable data

TL;DR

This paper investigates the quasineutral limit of the Vlasov-Poisson system for plasma ions with Sobolev regularity, establishing stability and well-posedness under Penrose stability conditions.

Contribution

It introduces a novel analysis of the quasineutral limit for Vlasov-Poisson systems with Penrose stable data, including a well-posedness theory for the limiting equation.

Findings

Established quasineutral limit under Penrose stability

Proved well-posedness for the limit equation with Dirac interaction

Extended analysis to Sobolev regularity data

Abstract

We study the quasineutral limit of a Vlasov-Poisson system that describes the dynamics of ions in a plasma. We handle data with Sobolev regularity under the sharp assumption that the profile of the initial data in the velocity variable satisfies a Penrose stability condition. As a by-product of our analysis, we obtain a well-posedness theory for the limit equation (which is a Vlasov equation with Dirac distribution as interaction kernel) for such data.