American Institute of Mathematical Sciences

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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

Yue-Jun Peng 1, and  Shu Wang 2,

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

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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