# American Institute of Mathematical Sciences

December  2016, 9(6): 2095-2111. doi: 10.3934/dcdss.2016086

## Quasineutral limit of the Euler-Poisson system under strong magnetic fields

 1 Department of Mathematics, Chongqing University, Chongqing 401331

Received  July 2015 Revised  September 2016 Published  November 2016

The quasineutral limit of the three dimensional compressible Euler-Poisson (EP) system for ions in plasma under strong magnetic field is rigorously studied. It is proved that as the Debye length and the Larmor radius tend to zero, the solution of the compressible EP system converges strongly to the strong solution of the one-dimensional compressible Euler-equation in the external magnetic field direction. Higher order approximation and convergence rates are also given and detailed studied.
Citation: Xueke Pu. Quasineutral limit of the Euler-Poisson system under strong magnetic fields. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2095-2111. doi: 10.3934/dcdss.2016086
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