Articles

BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

  • Zhensheng GAO ,
  • Zhong TAN
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  • 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;
    2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received date: 2016-09-20

  Revised date: 2017-06-12

  Online published: 2017-12-25

Supported by

The first author is supported by the Natural Science Key Foundation of Universities of Fujian Province (JZ160406) and Natural Science Foundation of Fujian Province (2015J01582).

Abstract

In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R3. We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u, d) is smooth up to time T provided that ∫0T║∇×u(t,·)║BMO(R3) + ║∇d(t,·)║L4(R3)8dt < ∞.

Cite this article

Zhensheng GAO , Zhong TAN . BLOW-UP CRITERION OF CLASSICAL SOLUTIONS FOR THE INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS[J]. Acta mathematica scientia, Series B, 2017 , 37(6) : 1632 -1638 . DOI: 10.1016/S0252-9602(17)30096-6

References

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