Comparison of the Bénard convection problem with its linearized problem

In this paper we derive an explicit decay bound for the L2L2 bound for the difference of the Bénard convection problem and its linearized problem if the Rayleigh number RaRa is less than the critical Rayleigh number RacRac predicted by the linear stability theory. In fact, if Ra0γ>0 regardless of the Prandtl number.