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Regularity criteria for Navier-Stokes-Allen-Cahn and related systems

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Abstract

We prove a regularity criterion for the 3D Navier-Stokes-Allen-Cahn system in a bounded smooth domain which improves the result obtained by Y. Li, S. Ding, and M. Huang [Discrete Contin. Dyn. Syst. Ser. B, 2016, 21(5): 1507–1523]. We also present a similar result to the 3D Navier-Stokes-Cahn-Hilliard system.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11171154, 11671193) and a project funded by the priority academic program development of Jiangsu higher education institutions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China

    Jishan Fan

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Fucai Li

Authors
  1. Jishan Fan
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  2. Fucai Li
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Correspondence to Fucai Li.

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Fan, J., Li, F. Regularity criteria for Navier-Stokes-Allen-Cahn and related systems. Front. Math. China 14, 301–314 (2019). https://doi.org/10.1007/s11464-019-0757-9

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  • DOI: https://doi.org/10.1007/s11464-019-0757-9

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