# American Institute of Mathematical Sciences

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

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.
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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