Incompressible type euler as scaling limit of compressible Euler-Maxwell equations

Abstract

In this paper, we study the convergence of time-dependent Euler-Maxwell equations to incompressible type Euler equations in a torus via the combined quasi-neutral and non-relativistic limit. For well prepared initial data, the local existence of smooth solutions to the limit equations is proved by an iterative scheme. Moreover, the convergences of solutions of the former to the solutions of the latter are justified rigorously by an analysis of asymptotic expansions and the symmetric hyperbolic property of the systems.