Optimal decay to the non-isentropic compressible micropolar fluids

Lvqiao liu; Lan Zhang

doi:10.3934/cpaa.2020207

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2020, Volume 19, Issue 9: 4575-4598. Doi: 10.3934/cpaa.2020207

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Optimal decay to the non-isentropic compressible micropolar fluids

Lvqiao liu^a, and
Lan Zhang^b, ,

a.
School of Mathematics and statistics, Wuhan University, Wuhan 430072, China
b.
Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China

^* Corresponding author
^* Corresponding author

Received: December 31, 2019

Revised: March 31, 2020

Published: June 2020

The second author is supported by NSF grant No.11971359, 11671309

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Abstract

In this paper, we are concerned with the large-time behavior of solutions to the Cauchy problem on the non-isentropic compressible micropolar fluid. For the initial data near the given equilibrium we prove the global well-posedness of classical solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. Moreover, it turns out that the density, the velocity and the temperature tend to the corresponding equilibrium state with rate $ (1+t)^{-3 / 4} $ in $ L^{2} $ norm and the micro-rotational velocity tends to the equilibrium state with the faster rate $ (1+t)^{-5 / 4} $ in $ L^{2} $ norm. The proof is based on the detailed analysis of the Green function and time-weighted energy estimates.

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Mathematics Subject Classification: Primary: 35Q35, 76D03; Secondary: 86A10.

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