Large-time behavior of solutions to the 3-D flow of a compressible viscous micropolar fluid with cylindrical symmetry

In this paper, we study the asymptotic behavior of global weak solutions in H-1 to the problem that describes compressible viscous and heat-conducting micropolar fluid flow in a three-dimensional domain bounded by two circular, coaxial, and infinite cylinders that present the solid thermoinsulated walls. In the thermodynamical sense, the fluid is perfect and polytropic. We prove that the global weak solution exists and converges to a steady state as time goes to infinity. We have been working under the assumption that the initial data are cylindrically symmetric and the initial total energy is sufficiently small.