Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 301–314 | Cite as

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

  • Jishan Fan
  • Fucai LiEmail author
Research Article


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.


Regularity criterion Navier-Stokes-Allen-Cahn system Navier-Stokes-Cahn-Hilliard system 


76T10 35Q30 35B44 


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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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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsNanjing Forestry UniversityNanjingChina
  2. 2.Department of MathematicsNanjing UniversityNanjingChina

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