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Existence, degenerate regularity and limit behavior of trajectory statistical solution for the 3D incompressible micropolar fluids flows with damping term

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Abstract

This article studies the existence, degenerate regularity and limit behavior of the trajectory statistical solution for a three-dimensional incompressible micropolar fluids flows with a damping term. The authors first prove the existence of the trajectory attractor and use it to construct the trajectory statistical solution. Then, they establish that the trajectory statistical solution possesses partial regularity provided that the associated Grashof number is small enough. Finally, they investigate the limiting behavior of the trajectory statistical solution as the damping term vanishes.

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Acknowledgements

The authors warmly thank the anonymous referee for his/her careful reading of the article and many pertinent remarks that lead to various improvements to this article.

Funding

Supported by NSF of China with No.11971356, 11271290, by NSF of Zhejiang Province with No.LY17A010011 and Ministerio de Ciencia e Innovación (Spain) with No. PID2021-122991NB-C21.

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Authors and Affiliations

  1. Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang Province, 325035, People’s Republic of China

    Caidi Zhao & Binbin Miao

  2. Departmento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/Tarfia s/n, 41012, Sevilla, Spain

    Tomás Caraballo

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  1. Caidi Zhao
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  2. Binbin Miao
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  3. Tomás Caraballo
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Correspondence to Caidi Zhao.

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Zhao, C., Miao, B. & Caraballo, T. Existence, degenerate regularity and limit behavior of trajectory statistical solution for the 3D incompressible micropolar fluids flows with damping term. Z. Angew. Math. Phys. 74, 141 (2023). https://doi.org/10.1007/s00033-023-02037-2

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  • DOI: https://doi.org/10.1007/s00033-023-02037-2

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