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 Bénard problem, for a fully ionized fluid. We show that, if the conduction-diffusion solution is linearly stable, it is asymptotically nonlinearly stable.