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

Xueke  Pu

doi:10.3934/dcdss.2016086

Article Contents

2016, Volume 9, Issue 6: 2095-2111. Doi: 10.3934/dcdss.2016086

This issue Previous Article Scattering theory for energy-supercritical Klein-Gordon equation Next Article The regularization of solution for the coupled Navier-Stokes and Maxwell equations

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

Xueke Pu^1,

1.
Department of Mathematics, Chongqing University, Chongqing 401331

Received: June 30, 2015

Revised: August 31, 2016

Published: November 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76X05.

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References

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