A regularity criterion for the three-dimensional nematic liquid crystal flow in terms of one directional derivative of the velocity

2011 ◽  
Vol 52 (3) ◽  
pp. 033102 ◽  
Author(s):  
Qiao Liu ◽  
Jihong Zhao ◽  
Shangbin Cui
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Directional Derivative ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Liquid Crystal Flow

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.

Three-dimensional coating flow of nematic liquid crystal on an inclined substrate

2015 ◽  
Vol 26 (5) ◽  
pp. 647-669 ◽  
Author(s):  
M. A. LAM ◽  
L. J. CUMMINGS ◽  
T.-S. LIN ◽  
L. KONDIC
Keyword(s):  
Free Surface ◽  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Linear Stability Theory ◽  
Newtonian Flow ◽  
Surface Evolution ◽  
Coating Flow

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring conditions at the substrate and free surface. Previous results have shown that there exist two-dimensional travelling wave solutions that translate down the substrate. In contrast to the analogous Newtonian flow, such solutions may be unstable to streamwise perturbations. Extending well-known results for Newtonian flow, we analyse the stability of the front with respect to transverse perturbations. Using full numerical simulations, we validate the linear stability theory and present examples of downslope flow of nematic liquid crystal in the presence of both transverse and streamwise instabilities.

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