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Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation |
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| Authors: | Yutong WANG Weike WANG |
| Affiliation: | 1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 220104, China2. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 220104, China |
| Abstract: | We investigate the Cauchy problem for the 3D magnetohydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method. |
| Keywords: | Magneto-hydrodynamics (MHD) equations degenerate dissipation global solution Green's function method frequency decomposition method |
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