论文标题
关于几乎laplacian磁扩散的2D MHD方程的全球规则性的评论
Remark on the global regularity of 2D MHD equations with almost Laplacian magnetic diffusion
论文作者
论文摘要
是否仅具有laplacian磁扩散（没有速度耗散）的二维（2D）不可压缩的磁性水力学（MHD）方程的经典解是一个困难的问题，都是一个困难的问题，仍然是一个困难的问题，并且保持完全开放。在本文中，我们建立了对2D不可压缩MHD方程的全球规律性，在整个空间中几乎具有拉普拉斯磁扩散。该结果可以被视为先前作品的进一步改进和概括。因此，我们的结果更接近具有标准拉普拉斯磁扩散的2D MHD方程上的全球规则性问题的分辨率。
Whether or not the classical solutions of the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only Laplacian magnetic diffusion (without velocity dissipation) are globally well-posed is a difficult problem and remains completely open. In this paper, we establish the global regularity of solutions to the 2D incompressible MHD equations with almost Laplacian magnetic diffusion in the whole space. This result can be regarded as a further improvement and generalization of the previous works. Consequently, our result is more closer to the resolution of the global regularity issue on the 2D MHD equations with standard Laplacian magnetic diffusion.
