# American Institute of Mathematical Sciences

January  2013, 12(1): 503-518. doi: 10.3934/cpaa.2013.12.503

## Incompressible type euler as scaling limit of compressible Euler-Maxwell equations

 1 College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China, China 2 College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022

Received  December 2010 Revised  April 2011 Published  September 2012

In this paper, we study the convergence of time-dependent Euler-Maxwell equations to incompressible type Euler equations in a torus via the combined quasi-neutral and non-relativistic limit. For well prepared initial data, the local existence of smooth solutions to the limit equations is proved by an iterative scheme. Moreover, the convergences of solutions of the former to the solutions of the latter are justified rigorously by an analysis of asymptotic expansions and the symmetric hyperbolic property of the systems.
Citation: Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure & Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503
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