On the Lyapunov function for the rotating Bénard problem

In this paper we study the nonlinear Lyapunov stability of the conduction-diffusion solution in a layer of a rotating Newtonian fluid, heated and salted from below. If we reformulate the nonlinear stability problem, projecting the initial perturbation evolution equations on some suitable orthogonal subspaces, 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 find that the nonlinear stability bound is nothing else but the critical Rayleigh number obtained solving the linear instability proble