Steady Convection in MHD Bénard Problem with Hall and Ion-Slip Effects

Abstract

In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting partially ionized fluid in a horizontal layer heated from below. The classical L 2 norm is too weak to evaluate some stabilizing or instabilizing effects of the electroanisotropic currents. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem in terms of the poloidal and toroidal scalar fields. In such a way, if instability occurs as stationary convection, we obtain the coincidence of linear and nonlinear stability bounds.