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A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum

Volume 115 / 2015

Zujin Zhang, Xian Yang Annales Polonici Mathematici 115 (2015), 165-177 MSC: Primary 35B65; Secondary 35Q35, 82D30. DOI: 10.4064/ap115-2-4

Abstract

We consider the Cauchy problem for the $3$D density-dependent incompressible flow of liquid crystals with vacuum, and provide a regularity criterion in terms of $\boldsymbol u$ and $\nabla {\boldsymbol d}$ in the Besov spaces of negative order. This improves a recent result of Fan–Li [Comm. Math. Sci. 12 (2014), 1185–1197].

Authors

  • Zujin ZhangSchool of Mathematics and Computer Science
    Gannan Normal University
    Ganzhou 341000, Jiangxi, P.R. China
    e-mail
  • Xian YangForeign Language Department
    Ganzhou Teachers College
    Ganzhou 341000, Jiangxi, P.R. China
    e-mail

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