Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line

Abstract

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the one-dimensional compressible isentropic micropolar fluid model in a half line <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}_{+}: = (0, \infty). $\end{document}</tex-math></inline-formula> We mainly investigate the unique existence, the asymptotic stability and convergence rates of stationary solutions to the outflow problem for this model. We obtain the convergence rates of global solutions towards corresponding stationary solutions if the initial perturbation belongs to the weighted Sobolev space. The proof is based on the weighted energy method by taking into account the effect of the microrotational velocity on the viscous compressible fluid.