On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method

AbstractIn this paper we use the Lyapunov direct method to study the nonlinear conditional stability of the Bénard problem with rotation. In particular, for Prandtl numbers greater than or equal to one, and for Taylor numbers less than or equal to 80π4, we prove the coincidence between the linear and nonlinear critical stability parameters. We also give some values of the attracting radius for the conditionally stable disturbances of the basic motion