Stability of stationary solutions for inflow problem on the micropolar fluid model

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half-line R+ := (0, infinity). We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the micropolar fluid model are time asymptotically stable under small H-1 perturbations in both the subsonic and degenerate cases. The microrotation velocity brings us some additional troubles compared with Navier-Stokes equations in the absence of the microrotation velocity. The proof of asymptotic stability is based on the basic energy method.