Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation
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We investigate the Cauchy problem for the 3D magneto-hydrodynamics 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.
KeywordsMagneto-hydrodynamics (MHD) equations degenerate dissipation global solution Green's function method frequency decomposition method
MSC35A01 35A22 35A25
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This work was supported in part by the National Natural Science Foundation of China (Grant No. 11771284).