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Remarks on the regularity criterion for the nematic liquid crystal flows in R3

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  • Qian, Chenyin

Abstract

In this paper, we investigate the regularity criteria for the 3D nematic liquid crystal flows in terms of the components of the velocity u or the gradient of the velocity field ∇u. More precisely, the anisotropic integrability regularity criterion to the 3D nematic liquid crystal flows involving ∂iu,i=1,2,3 is obtained firstly, and then it is proved that the solution is regular if u3, ω3 or ∂3u3, ω3 satisfies the Prodi–Serrin type conditions.

Suggested Citation

  • Qian, Chenyin, 2016. "Remarks on the regularity criterion for the nematic liquid crystal flows in R3," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 679-689.
    • Handle: RePEc:eee:apmaco:v:274:y:2016:i:c:p:679-689
    DOI: 10.1016/j.amc.2015.11.007
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