scholarly journals On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

2020 ◽  
Vol 19 (11) ◽  
pp. 5219-5238
Author(s):  
Yang Liu ◽  
◽  
Xin Zhong ◽  
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
The Cauchy Problem ◽  
Nematic Liquid Crystal Flows

scholarly journals Regularity and uniqueness for a class of solutions to the hydrodynamic flow of nematic liquid crystals

2016 ◽  
Vol 14 (04) ◽  
pp. 523-536 ◽  
Author(s):  
Tao Huang
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Weak Solutions ◽  
Nematic Liquid Crystals ◽  
Regularity Criterion ◽  
Liquid Crystal Flow ◽  
The Cauchy Problem

In this paper, we establish an [Formula: see text]-regularity criterion for any weak solution [Formula: see text] to the nematic liquid crystal flow (1.1) such that [Formula: see text] for some [Formula: see text] and [Formula: see text] satisfying the condition (1.2). As consequences, we prove the interior smoothness of any such a solution when [Formula: see text] and [Formula: see text]. We also show that uniqueness holds for the class of weak solutions [Formula: see text] the Cauchy problem of the nematic liquid crystal flow (1.1) that satisfy [Formula: see text] for some [Formula: see text] and [Formula: see text] satisfying (1.2).

scholarly journals Regularity Criterion for the 3D Nematic Liquid Crystal Flows

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Regularity Criterion ◽  
Hydrodynamic Theory ◽  
Nematic Liquid Crystal Flows

We study the hydrodynamic theory of liquid crystals. We prove a logarithmically improved regularity criterion for two simplified Ericksen-Leslie systems.

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