Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry

Abstract

This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of \begin{document}$ R^3 $\end{document} bounded with two coaxial cylinders that present the solid thermo-insulated walls, which is in a thermodynamical sense perfect and polytropic. Compared with the classical Navier-Stokes equations, the angular velocity \begin{document}$ w $\end{document} in this model brings benefit that is the damping term -\begin{document}$ uw $\end{document} can provide extra regularity of \begin{document}$ w $\end{document}. At the same time, the term \begin{document}$ uw^2 $\end{document} is bad, it increases the nonlinearity of our system. Moreover, the regularity and exponential stability in \begin{document}$ H^4 $\end{document} also are proved.