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

In this paper, we consider the global regularity of 2D magnetic Benard 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 by D-2 and D-3 two Fourier multipliers whose symbols m(2) and m(3) are respectively given by m(2)(xi) equivalent to vertical bar xi vertical bar(2) log(e + vertical bar xi vertical bar(|2))(beta) and m(3)(xi) = vertical bar xi vertical bar(2) log(e + vertical bar xi vertical bar(2))gamma. In another way, we generalize the previous case and the magnetic diffusion and thermal diffusivity are separately given by L-2 and L-3 two Fourier multipliers whose symbols m2 and m3 are respectively given by m(2) = vertical bar xi vertical bar(2)g(2)(xi) and m(3) = vertical bar xi vertical bar(2)g(3)(xi), where g(j) = g(j)(vertical bar xi vertical bar) (j = 2, 3) are two radial non-decreasing smooth functions.