Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters

Yue-Jun Peng; Shu Wang

doi:10.3934/dcds.2009.23.415

Article Contents

2009, Volume 23, Issue 1&2: 415-433. Doi: 10.3934/dcds.2009.23.415

This issue Previous Article A spectral approach to the indirect boundary control of a system of weakly coupled wave equations Next Article Non-linear electromagnetism and special relativity

Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters

Yue-Jun Peng^1, and
Shu Wang^2,

1.
Laboratoire de Mathématiques, CNRS UMR 6620, Université Clermont-Ferrand 2, 63177 Aubière cedex
2.
College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022

Received: November 30, 2007

Revised: March 31, 2008

Published: April 2009

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Abstract

This work is concerned with the two-fluidEuler-Maxwell equations for plasmas with small parameters. We study,by means of asymptotic expansions, the zero-relaxation limit, thenon-relativistic limit and the combined non-relativistic and quasi-neutrallimit. For each limit with well-prepared initial data, we show theexistence and uniqueness of an asymptotic expansion up to any order. Forgeneral data, an asymptotic expansion up to order 1 of thenon-relativistic limit is constructed by taking into account the initiallayers. Finally, we discuss the justification of the limits.

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Mathematics Subject Classification: 35B40, 35C20, 35L60, 35Q35.

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