On the Lyapunov function for the rotating Benard problem

Abstract

In this paper we study the nonlinear Lyapunov stability of the conduction-diusion solution in a layer of a rotating Newtonian uid, heated and salted from below.If we reformulate the nonlinear stability problem, projecting the ini-tial perturbation evolution equations on some suitable orthogonal sub-spaces, we preserve the contribution of the Coriolis term, and jointly all the nonlinear terms vanish.We prove that, if the principle of exchange of stabilities holds, the linear and nonlinear stability bounds are equal. We nd that the non- linear stability bound is nothing else but the critical Rayleigh number obtained solving the linear instability problem.