Stability of the composite wave for the inflow problem on the micropolar fluid model

Abstract

In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in half line $\mathbb{R}_{+}:=(0, \infty).$ Inspired by the relationship between the micropolar fluid model and Navier-Stokes system, we can prove that the composite wave consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem on micropolar fluid model is time-asymptotically stable. Meanwhile, we obtain the global existence of solutions based on the basic energy method.