Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

Uniform local well-posedness and regularity criterion for the density-dependent incompressible flow of liquid crystals

Pages: 1185 – 1197

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n7.a1

Authors

Jishan Fan (Department of Applied Mathematics, Nanjing Forestry University, Nanjing, China)

Fucai Li (Department of Mathematics, Nanjing University, Nanjing, China)

Abstract

In this paper we first prove the uniform local well-posedness for the density-dependent incompressible flow of liquid crystals in the whole space $\mathbb{R}^3$. Next, we provide a regularity criterion for the strong solution when the initial density may contain vacuum.

Keywords

density-dependent incompressible flow, liquid crystals, vacuum, uniform local well-posedness, regularity criterion

2010 Mathematics Subject Classification

35Q30, 76D03, 82D30

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