数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 395-404.doi: 10.1016/S0252-9602(17)30010-3

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GLOBAL REGULARITY TO THE 2D INCOMPRESSIBLE MHD WITH MIXED PARTIAL DISSIPATION AND MAGNETIC DIFFUSION IN A BOUNDED DOMAIN

于海波   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
  • 收稿日期:2015-07-07 修回日期:2016-06-11 出版日期:2017-04-25 发布日期:2017-04-25
  • 作者简介:Haibo YU,E-mail:yuhaibo2049@tom.com
  • 基金资助:

    The author was supported by the Scientific Research Funds of Huaqiao University (14BS309) and the National Natural Science Foundation of China (11526091).

GLOBAL REGULARITY TO THE 2D INCOMPRESSIBLE MHD WITH MIXED PARTIAL DISSIPATION AND MAGNETIC DIFFUSION IN A BOUNDED DOMAIN

Haibo YU   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
  • Received:2015-07-07 Revised:2016-06-11 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    The author was supported by the Scientific Research Funds of Huaqiao University (14BS309) and the National Natural Science Foundation of China (11526091).

摘要:

This article considers the global regularity to the initial——boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for ux and by, which are estimated by ▽×ux and ▽×by, respectively. Then, we establish the global estimates for ▽×u and ▽×b.

关键词: Global classical solution, incompressible MHD, initial--boundary value problem, partial dissipation

Abstract:

This article considers the global regularity to the initial——boundary value problem for the 2D incompressible MHD with mixed partial dissipation and magnetic diffusion. To overcome the difficulty caused by the vanishing viscosities, we first establish the elliptic system for ux and by, which are estimated by ▽×ux and ▽×by, respectively. Then, we establish the global estimates for ▽×u and ▽×b.

Key words: Global classical solution, incompressible MHD, initial--boundary value problem, partial dissipation