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

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January & February 2009, 23(1&2): 415-433. doi: 10.3934/dcds.2009.23.415

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

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

Received December 2007 Revised April 2008 Published September 2008

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

Keywords: formal limits, initial layer expansion, Compressible Euler-Maxwell equations, asymptotic expansion.

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

Citation: Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415

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