On the regularity criteria for liquid crystal flows

  • Lingling Zhao
  • Fengquan LiEmail author


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 \(u_{3}, \nabla _{h}d\in {L^{p}(0,T; L^{q}(R^{3}))}\), \(\frac{2}{p}+\frac{3}{q}\le {\frac{3}{4}+\frac{1}{2q}}(q>{\frac{10}{3}})\).


Liquid crystal Regularity criteria Velocity component Orientation field component 

Mathematics Subject Classification

35B65 35Q35 



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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Dalian University of TechnologyDalianChina

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