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Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain

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Abstract

In this paper, we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain. The prominent character of the governing model is the presence of the microstructure, a linear coupling structure involving derivatives of the velocity fields, which along with the lack of spin viscosity brings several challenges to the analysis. By exploiting the two-tier energy method developed in Guo and Tice (Arch Ration Mech Anal, 2013), we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal boundary. Moreover, we show that the solution converges to the steady state at an almost exponential rate as time goes to infinity. One of the main ingredients in our analysis, compared with previous works on micropolar fluids, is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition, and the coupling between the fluid velocity and the vorticity of angular velocity.

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Acknowledgements

Zefu Feng was supported by National Natural Science Foundation of China (Grant No. 12101095), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202100517), the Research Project of Chongqing Education Commission (Grant No. CXQT21014), the Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-msxmX0224), and the Grant of Chongqing Young Experts’ Workshop. Guangyi Hong was supported by National Natural Science Foundation of China (Grant No. 12201221) and the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515111038). Changjiang Zhu was supported by National Natural Science Foundation of China (Grant Nos. 12171160 and 11831003) and the Guangdong Provincial Key Laboratory of Human Digital Twin (Grant No. 2022B1212010004). The authors sincerely thank the referees for all the helpful comments and useful suggestions on the manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Zefu Feng

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Guangyi Hong & Changjiang Zhu

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  1. Zefu Feng
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  2. Guangyi Hong
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  3. Changjiang Zhu
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Correspondence to Changjiang Zhu.

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Feng, Z., Hong, G. & Zhu, C. Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain. Sci. China Math. (2024). https://doi.org/10.1007/s11425-022-2185-0

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