Global regularity of 2D magnetic Bénard fluid equations with zero kinematic viscosity, almost Laplacian magnetic diffusion and thermal diffusivity. Issue 8 (24th May 2022) - Ma, Liangliang
ABSTRACT: 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 by D 2 and D 3 two Fourier multipliers whose symbols m 2 and m 3 are respectively given by m 2 ( ξ ) ≡ | ξ | 2 log ⁡ ( e + | ξ | 2 ) β and m 3 ( ξ ) ≡ | ξ | 2 log ⁡ ( e + | ξ | 2 ) γ . 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 m 2 and m 3 are respectively given by m 2 = | ξ | 2 g 2 ( ξ ) and m 3 = | ξ | 2 g 3 ( ξ ), where g j = g j ( | ξ | ) ( j = 2, 3 ) are two radial non-decreasing smooth functions.