### Electronic Research Archive

2020, Issue 2: 861-878. doi: 10.3934/era.2020045

# Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry

• Received: 01 January 2020 Revised: 01 April 2020
• Primary: 35Q35, 76N10; Secondary: 35Q30

• This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of $R^3$ bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a thermodynamical sense perfect and polytropic. We prove that the regularity and the exponential stability in $H^2$.

Citation: Zhi-Ying Sun, Lan Huang, Xin-Guang Yang. Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry[J]. Electronic Research Archive, 2020, 28(2): 861-878. doi: 10.3934/era.2020045

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• This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of $R^3$ bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a thermodynamical sense perfect and polytropic. We prove that the regularity and the exponential stability in $H^2$.

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