Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries

TL;DR

This paper investigates the behavior of the Euler-Poisson system for ions in a three-dimensional domain with boundaries, extending previous one-dimensional boundaryless results to more realistic settings.

Contribution

It extends the analysis of the quasineutral limit of the Euler-Poisson system to three-dimensional domains with boundaries, building on prior one-dimensional boundaryless work.

Findings

Established the quasineutral limit in 3D with boundaries

Extended previous 1D boundaryless results to 3D with boundaries

Provided mathematical framework for plasma modeling in bounded domains

Abstract

We study the quasineutral limit of the isothermal Euler-Poisson system describing a plasma made of ions and massless electrons. The analysis is achieved in a domain of $\R^3$ and thus extends former results by Cordier and Grenier [Comm. Partial Differential Equations, 25 (2000), pp.~1099--1113], who dealt with the same problem in a one-dimensional domain without boundary.