Decay estimates of solutions to the compressible micropolar fluids system in R3

Abstract This work is concerned with the compressible micropolar fluids system in three–dimensional space. We consider the asymptotic behavior of the solution to the Cauchy problem near the constant equilibrium state provided that the initial perturbation is sufficiently small. Under some assumptions of the initial data, we show that the solution of the Cauchy problem converges to its constant equilibrium state at the exact same L 2 –decay rates as the linearized equations, which shows the convergence rates are optimal. The proof is based on the spectral analysis of the semigroup generated by the linearized equations and the nonlinear energy estimates.