scholarly journals A Serrin type criterion for incompressible hydrodynamic flow of liquid crystals in dimension three

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1445-1456
Author(s):  
Bingyuan Huang
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Heat Flow ◽  
Nematic Liquid Crystal ◽  
Open Subset ◽  
Harmonic Map ◽  
System Modeling ◽  
Strong Solutions ◽  
Type Criterion ◽  
Leslie System

In the paper, we establish a Serrin type criterion for strong solutions to a simplified densitydependent Ericksen-Leslie system modeling incompressible, nematic liquid crystal materials in dimension three. The density may vanish in an open subset of ?. As a byproduct, we establish the Serrin type criterion for heat flow of harmonic map whose gradients belong to Lrx Lst, where 2/s + 3/r ? 1, for 3 < r ? ?.

New structure induced by elastic anisotropy in cylindrical nematic liquid crystal

2017 ◽  
Vol 13 (2) ◽  
pp. 4705-4717
Author(s):  
Zhang Qian ◽  
Zhou Xuan ◽  
Zhang Zhidong
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Nematic Liquid Crystal ◽  
Elastic Anisotropy ◽  
Nematic Liquid Crystals ◽  
Gennes Theory

Basing on Landau–de Gennes theory, this study investigated the chiral configurations of nematic liquid crystals confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls. When the elastic anisotropy (L2/L1) is large enough, a new structure results from the convergence of two opposite escape directions of the heterochiral twist and escape radial (TER) configurations. The new defect presents when L2/L1≥7 and disappears when L2/L1<7. The new structure possesses a heterochiral hyperbolic defect at the center and two homochiral radial defects on both sides. The two radial defects show different chiralities.

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.

The breathers in nematic liquid crystals under applied electric field

2019 ◽  
Vol 33 (26) ◽  
pp. 1950319
Author(s):  
Yan Li ◽  
Xiaobo Lu ◽  
Chunfeng Hou
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Electric Field ◽  
Nematic Liquid Crystal ◽  
Dynamic Equation ◽  
Applied Electric Field ◽  
Deflection Angle ◽  
Breather Solution ◽  
The Relationship ◽  
Sg Equation

In this paper, we study the twist of the nematic liquid crystal molecules under the applied electric field. The dynamic equation of the twisted molecules is derived. It is proved to be a kind of sine-Gordon (SG) equation. We obtain the breather solution of the equation and confirm that the deflection angles of the twisted molecules can distribute in the form of breathers. We give the relationship between the molecular deflection angle and the breather frequency, and discuss the effect of electric field on breather shape and breather frequency.

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