数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1655-1677.

• 论文 • 上一篇    下一篇

THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

张志朋1,2   

  1. 1 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    2 Department of Mathematics, Nanjing University, Nanjing 210093, China
  • 收稿日期:2017-04-24 修回日期:2017-10-16 出版日期:2018-12-25 发布日期:2018-12-28
  • 作者简介:Zhipeng ZHANG,E-mail:zhpzhp@aliyun.com
  • 基金资助:
    This paper is supported by the National Natural Science Foundation of China (11671193) and the China Scholarship Council.

THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

Zhipeng ZHANG1,2   

  1. 1 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    2 Department of Mathematics, Nanjing University, Nanjing 210093, China
  • Received:2017-04-24 Revised:2017-10-16 Online:2018-12-25 Published:2018-12-28
  • Supported by:
    This paper is supported by the National Natural Science Foundation of China (11671193) and the China Scholarship Council.

摘要: In this paper, we establish the existence of the global weak solutions for the nonhomogeneous incompressible magnetohydrodynamic equations with Navier boundary conditions for the velocity field and the magnetic field in a bounded domain Ω ⊂ R3. Furthermore, we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weak solutions converge to the strong one of the ideal nonhomogeneous incompressible magnetohydrodynamic equations in energy space.

关键词: nonhomogeneous incompressible MHD equations, Navier boundary conditions, inviscid and non-resistive limit

Abstract: In this paper, we establish the existence of the global weak solutions for the nonhomogeneous incompressible magnetohydrodynamic equations with Navier boundary conditions for the velocity field and the magnetic field in a bounded domain Ω ⊂ R3. Furthermore, we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weak solutions converge to the strong one of the ideal nonhomogeneous incompressible magnetohydrodynamic equations in energy space.

Key words: nonhomogeneous incompressible MHD equations, Navier boundary conditions, inviscid and non-resistive limit