Quasi-neutral limit of Euler-Poisson system of compressible fluids coupled to a magnetic field

TL;DR

This paper studies the behavior of a 3D Euler-Poisson system coupled with magnetic fields as the Debye length approaches zero, showing convergence to incompressible magnetohydrodynamic equations with proven rates.

Contribution

It establishes the rigorous quasi-neutral limit of the Euler-Poisson system coupled with magnetic fields, including convergence rates and conditions for smooth solutions.

Findings

Solutions exist and are unique in the quasi-neutral limit.

Smooth solutions converge to incompressible MHD solutions.

Convergence rate is explicitly established.

Abstract

In this paper, we consider the quasi-neutral limit of a three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model have unique smooth solutions existing in the time interval where the ideal incompressible magnetohydrodynamic equations has smooth solution. Meanwhile, it is proved that smooth solutions converge to solutions of incompressible magnetohydrodynamic equations with a sharp convergence rate in the process of quasi-neutral limit.