On the nonlinear stability of the MHD anisotropic Bénard problem

In this paper, by the Lyapunov direct method, we study the nonlinear Lyapunov stability of the conduction–diffusion solution of the anisotropic magnetic Benard problem, for a fully ionized fluid. We show that, if the conduction–diffusion solution is linearly stable, it is asymptotically nonlinearly stable.