Stability and large-time behavior of the inviscid Boussinesq system for the micropolar fluid with damping

Abstract

In this paper, we consider the three-dimensional inviscid Boussinesq system for the micropolar fluid in porous media. We proved the global well-posedness and large time behavior of solutions in the whole space R3. Precisely, when the H3-norm of initial data is small, but the higher-order derivatives can be arbitrarily large, the system is globally well-posed by the pure energy method. Moreover, by a set of mature negative Sobolev and Besov space interpolation methods, the Lp − L2 (1 ≤ p ≤ 2) type of the optimal time decay rates are obtained without any smallness assumption on the Lp norm of the initial data. Our results mathematically explain the stability of the system in an unbounded domain.