Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations*

Abstract

In this paper, the convergence of time-dependent Euler-Maxwell equations tocompressible Euler-Poisson equations in a torus via the non-relativistic limit is studied.The local existence of smooth solutions to both systems is proved by using energy estimates for first order symmetrizable hyperbolic systems. For well prepared initial data theconvergence of solutions is rigorously justified by an analysis of asymptotic expansions upto any order. The authors perform also an initial layer analysis for general initial data andprove the convergence of asymptotic expansions up to first order.

Keywords

Euler-Maxwell equations / Compressible Euler-Poisson equations / Non-relativistic limit / Asymptotic expansion and convergence / 35B40 / 35C20 / 35L60 / 35Q35

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