数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 805-818.doi: 10.1016/S0252-9602(18)30785-9

• 论文 • 上一篇    下一篇

CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS

徐鑫   

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2017-03-14 修回日期:2017-10-16 出版日期:2018-06-25 发布日期:2018-06-25
  • 作者简介:Xin XU,E-mail:xuxinaboy@126.com
  • 基金资助:

    The research is supported by Postdoctoral Science Foundation of China through Grant 2017M610818.

CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS

Xin XU   

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2017-03-14 Revised:2017-10-16 Online:2018-06-25 Published:2018-06-25
  • Supported by:

    The research is supported by Postdoctoral Science Foundation of China through Grant 2017M610818.

摘要:

We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t=0. The strong convergence results only hold outside the initial layer.

关键词: Zero dielectric constant limit, full compressible magnetohydrodynamic equation, initial layer

Abstract:

We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t=0. The strong convergence results only hold outside the initial layer.

Key words: Zero dielectric constant limit, full compressible magnetohydrodynamic equation, initial layer