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Optimal decay to the non-isentropic compressible micropolar fluids

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

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  • 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.

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


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