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Exponential stability for the compressible micropolar fluid with cylinder symmetry in R3

This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of R3 bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a perfect and polytropic thermodynamical sense. We prove that cylindrically symmetric solutions decay to a constant exponentially as time goes to infinity based on the assumptions that the initial total energy is sufficiently small and initial data are sufficiently smooth cylindrically symmetric functions.

micropolar fluid, generalized solution, cylinder symmetry, exponential stability

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