Global regularity of the 2D magnetohydrodynamic equations with fractional anisotropic dissipation |
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| Institution: | 1. Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, PR China;2. The Graduate School of China Academy of Engineering Physics, PO Box 2101, Beijing 100088, PR China;1. Department of Mathematics, Oklahoma State University, 401 Mathematical Sciences, Stillwater, OK 74078, USA;2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China;3. Department of Mathematics and Statistics, Jiangsu Normal University, 101 Shanghai Road, Xuzhou 221116, Jiangsu, PR China |
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| Abstract: | This paper is dedicated to establishing the global regularity for the two dimensional magnetohydrodynamic equations with fractional anisotropic dissipation when the fractional powers are restricted to some certain ranges. In addition, the global regularity results for the two dimensional magnetohydrodynamic equations with partial dissipation are also obtained. Consequently, these results bring us more closer to the resolution of the global regularity problem on the two dimensional magnetohydrodynamic equations with standard Laplacian magnetic diffusion. |
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| Keywords: | MHD equations Fractional dissipation Partial dissipation Global regularity |
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