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On the regularity criteria for liquid crystal flows

  • Lingling Zhao
  • Fengquan Li
Article
  • 20 Downloads

Abstract

In this paper, we show a regularity criteria for three-dimensional nematic liquid crystal flows. More precisely, we prove that the weak solution (ud) can be extended beyond T, provided \(u_{3}, \nabla _{h}d\in {L^{p}(0,T; L^{q}(R^{3}))}\), \(\frac{2}{p}+\frac{3}{q}\le {\frac{3}{4}+\frac{1}{2q}}(q>{\frac{10}{3}})\).

Keywords

Liquid crystal Regularity criteria Velocity component Orientation field component 

Mathematics Subject Classification

35B65 35Q35 

Notes

Acknowledgements

This work was partly supported by NSFC (Nos. 11571057, 11671067). The first author is also very grateful to Dr Wendong Wang for his suggestion and help.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dalian University of TechnologyDalianChina

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