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Global Regularity of 3D Nonhomogeneous Incompressible Micropolar Fluids

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Abstract

This paper is concerned with the global well-posedness of strong and classical solutions for the 3D nonhomogeneous incompressible micropolar equations with vacuum. We prove that the problem (1.1)–(1.5) has a unique global strong/classical solution \((\rho,u,w)\), provided \(\mu_{1}\) is sufficiently large, or \(\|\rho_{0}\|_{L^{\infty}}\) or \(\|\rho_{0}^{1/2}u_{0}\| ^{2}_{L^{2}}+\|\rho_{0}^{1/2}w_{0}\|^{2}_{L^{2}}\) is small enough.

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Acknowledgements

The authors would like to thank the anonymous referees and the editors for their valuable suggestions and comments, which improved the results and the quality of the paper. Zhang was partially supported by National Natural Science Foundation of China (Grant No. 11701192), the Natural Science Foundation of Fujian Province of China (Grant No. JAT160026) and the Scientific Research Funds of Huaqiao University (Grant No. 14BS319 & 15BS201). Zhu was partially supported by Natural Science Foundation of Zhejiang Province of China (Grant No. LQ17A010006).

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P.R. China

    Peixin Zhang

  2. Department of Mathematics, Jiaxing University, Jiaxing, 314001, P.R. China

    Mingxuan Zhu

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  1. Peixin Zhang
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Correspondence to Mingxuan Zhu.

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Zhang, P., Zhu, M. Global Regularity of 3D Nonhomogeneous Incompressible Micropolar Fluids. Acta Appl Math 161, 13–34 (2019). https://doi.org/10.1007/s10440-018-0202-1

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