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

doi:10.1016/S0252-9602(17)30010-3

Acta mathematica scientia,Series B ›› 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

Haibo YU

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).

Abstract

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 u_x and b_y, which are estimated by ▽×u_x and ▽×b_y, respectively. Then, we establish the global estimates for ▽×u and ▽×b.

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

Haibo YU. GLOBAL REGULARITY TO THE 2D INCOMPRESSIBLE MHD WITH MIXED PARTIAL DISSIPATION AND MAGNETIC DIFFUSION IN A BOUNDED DOMAIN[J].Acta mathematica scientia,Series B, 2017, 37(2): 395-404.

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

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