Comparison of the Benard convection problem with its linearized problem

Abstract

In this paper we derive in explicit decay bound for L-2 bound for the difference of the Benard convection problem and its linearized problem if the Rayleigh number Ra is less than the critical Rayleigh number Ra-c predicted by the linear stability theory. In fact, if Ra Ra-c, it is shown that this L-2 bound for the difference decays exponentially in time for the initial amplitude O(e(2 gamma t)) with gamma > 0 regardless of the Prandtl number. (C) 2007 Elsevier Ltd. All rights reserved.