The Euler--Maxwell system for electrons: global solutions in $2D$

TL;DR

This paper proves the global stability of a constant neutral background in a 2D Euler-Maxwell system modeling electron plasma dynamics, contributing to the understanding of plasma behavior in simplified models.

Contribution

It establishes the first global stability result for the 2D Euler-Maxwell system for electrons, a simplified plasma model, under small perturbations.

Findings

Global stability of the neutral background in 2D

Mathematical proof of stability for the Euler-Maxwell system

Advances understanding of plasma dynamics in simplified models

Abstract

A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid" Euler--Maxwell model for electrons, in 2 spatial dimensions, and prove global stability of a constant neutral background.