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Global regularity results for the D magnetic Bénard system with mixed partial viscosity

ABSTRACT This paper studies the global regularity for the D magnetic Bénard system with mixed partial viscosity. More precisely, we first show the global regularity for the D magnetic Bénard system with zero thermal diffusivity by a well-known property of Hardy space and BMO. Moreover, resorting to the method of the local-in-time analysis, the global regularity for the D magnetic Bénard system with zero thermal diffusivity and horizontal magnetic diffusion as well as vertical magnetic diffusion are also obtained.