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In this paper, we consider the global regularity of 2D magnetic Bénard fluid equations with almost magnetic diffusion and thermal diffusivity and without kinematic viscosity. We focus on this goal in two ways. In one way, the magnetic diffusion and thermal diffusivity are separately given byandtwo Fourier multipliers whose symbolsandare respectively given byand. In another way, we generalize the previous case and the magnetic diffusion and thermal diffusivity are separately given byandtwo Fourier multipliers whose symbolsandare respectively given byand, whereare two radial non-decreasing smooth functions.

Global regularity of 2D magnetic Bénard fluid equations with zero kinematic viscosity, almost Laplacian magnetic diffusion and thermal diffusivity