Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion
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DOI：
10.1016/j.aim.2010.08.017
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发表时间：
2009-01
影响因子：
1.7
通讯作者：
C. Cao;Jiahong Wu
中科院分区：
文献类型：
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作者：
C. Cao;Jiahong Wu
无全耗散和无磁扩散的二维不可压缩MHD方程的经典解能否产生有限时间奇性是一个难题。本文的一个主要结果是建立了混合部分耗散和磁扩散的MHD方程经典解的整体正则性。此外，还得到了只具有磁扩散的二维MHD方程弱解的整体存在性、条件正则性和唯一性。
Whether or not classical solutions of the 2D incompressible MHD equations without full dissipation and magnetic diffusion can develop finite-time singularities is a difficult issue. A major result of this paper establishes the global regularity of classical solutions for the MHD equations with mixed partial dissipation and magnetic diffusion. In addition, the global existence, conditional regularity and uniqueness of a weak solution is obtained for the 2D MHD equations with only magnetic diffusion.