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September  2020, 19(9): 4575-4598. doi: 10.3934/cpaa.2020207

## Optimal decay to the non-isentropic compressible micropolar fluids

 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

Received  January 2020 Revised  April 2020 Published  June 2020

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

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.

Citation: Lvqiao liu, Lan Zhang. Optimal decay to the non-isentropic compressible micropolar fluids. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4575-4598. doi: 10.3934/cpaa.2020207
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