The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
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DOI：
10.1137/130937718
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
C. Cao;Jiahong Wu;Baoquan Yuan
中科院分区：
文献类型：
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作者：
C. Cao;Jiahong Wu;Baoquan Yuan
This paper examines the global (in time) regularity of classical solutions to the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator $(-\Delta)^\beta$. We establish the global regularity for the case when $\beta>1$. This result significantly improves previous work which requires $\beta>\frac{3}{2}$ and brings us closer to the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely, the case when $\beta=1$.
