Large time behavior of weak solutions to d-dimensional micropolar Rayleigh-Bénard problem

Abstract

This paper focuses on the large time behavior of the global weak solutions to the micropolar Rayleigh-Bénard problem near a hydrostatic equilibrium in Rd with d=2,3. We obtain the optimal decay rates (t+1)−d4(2q−1) and (t+1)−12−d4(2q−1) of the L2 norm of a solution and its first derivatives to this system with full dissipation, or with zero angular viscosity. Moreover, the enhanced decay rate (t+1)−12−d4(2q−1) of the L2 norm of the micro-rotational velocity is also established.