Optimal time decay of the compressible micropolar fluids

This paper primarily studies the large-time behavior of solutions to the Cauchy problem on the compressible micropolar fluid system which is a generalization of the classical Navier-Stokes system. The asymptotic stability of the steady state with the strictly positive constant density, the vanishing velocity, and micro-rotational velocity is established under small perturbation in regular Sobolev space. Moreover, it turns out that both the density and the velocity tend time-asymptotically to the corresponding equilibrium state with rate (1 +t)(-3/4) in L-2 and the micro-rotational velocity also tends to the equilibrium state with the faster rate (1 +t)(-5/4) in L-2 norm. The proof is based on the spectrum analysis and time-weighted energy estimate. (C) 2016 Elsevier Inc. All rights reserved.