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

Lan Huang; Zhiying Sun; Xin-Guang Yang; Alain Miranville

doi:10.3934/cpaa.2022033

Article Contents

2022, Volume 21, Issue 5: 1595-1620. Doi: 10.3934/cpaa.2022033

This issue Previous Article Shock polars for non-polytropic compressible potential flow Next Article Random attractors for non-autonomous stochastic Brinkman-Forchheimer equations on unbounded domains

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

1.
College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2.
Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China
3.
Laboratoire de Mathématiques et Applications, UMR CNRS 7348-SP2MI, Université de Poitiers, Boulevard Marie et Pierre Curie-Téléport 2 86962, Chasseneuil Futuroscope Cedex, France

^* Corresponding Author
^* Corresponding Author

Received: September 2021

Revised: January 2022

Early access: February 2022

Published: May 2022

This paper was partially supported by the NSFC (No. 11501199), the Young Key Teachers Project in Higher Vocational Colleges of Henan Province (No. 2020GZGG109), Young Backbone Teachers in Henan Province (No. 2018GGJS039), Incubation Fund Project of Henan Normal University (No. 2020PL17), Henan Overseas Expertise Introduction Center for Discipline Innovation (No. CXJD2020003)

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Abstract

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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Mathematics Subject Classification: Primary: 35B40; Secondary: 35Q35.

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