Abstract
This paper deals with the Cauchy problem to the 3D system of incompressible magnetic Bénard fluids. We prove that as the initial data satisfy ‖u0‖H1(R3)2+‖b0‖H1(R3)2+‖θ0‖H1(R3)2≤ε, where ε is a suitably small positive number, then the 3D magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity admit global smooth solutions.
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