ON THE STABILITY OF THE ROTATING BENARD PROBLEM

In this paper we study the nonlinear Lyapunov stability of the conduction-diffusion solution of the rotating Benard problem. We provide a method for a derivation of the optimum nonlinear stability bound. It allows us to derive a linearization principle in a larger sense, i.e. to prove that, if the principle of exchange of stabilities holds, the linear and nonlinear stability bounds are equal. After reformulating the perturbation evolution equations in a suitable equivalent form, we derive the appropriate Lyapunov function and for the first time we find that the nonlinear stability bound is nothing else but the critical Rayleigh number obtained solving the linear instability problem of the conduction-diffusion solution.