This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of $ R^3 $ 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 $ w $ in this model brings benefit that is the damping term -$ uw $ can provide extra regularity of $ w $. At the same time, the term $ uw^2 $ is bad, it increases the nonlinearity of our system. Moreover, the regularity and exponential stability in $ H^4 $ also are proved.
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