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 On the uniqueness of weak solutions to the Ericksen–Leslie liquid crystal model in ℝ2

2016 ◽  
Vol 26 (04) ◽  
pp. 803-822 ◽  
Author(s):  
Jinkai Li ◽  
Edriss S. Titi ◽  
Zhouping Xin
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Liquid Crystal ◽  
Weak Solutions ◽  
Energy Estimates ◽  
Unique Weak Solution ◽  
The Cauchy Problem ◽  
Crystal Model ◽  
Main Ideas ◽  
Leslie System

This paper concerns the uniqueness of weak solutions to the Cauchy problem to the Ericksen–Leslie system of liquid crystal models in [Formula: see text], with both general Leslie stress tensors and general Oseen–Frank density. It is shown here that such a system admits a unique weak solution provided that the Frank coefficients are close to some positive constant. One of the main ideas of our proof is to perform suitable energy estimates at the level one order lower than the natural basic energy estimates for the Ericksen–Leslie system.

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.

Orientation, interaction and laser assisted self-assembly of organic single-crystal micro-sheets in a nematic liquid crystal

Soft Matter ◽  
2015 ◽  
Vol 11 (38) ◽  
pp. 7674-7679 ◽  
Author(s):  
M. V. Rasna ◽  
K. P. Zuhail ◽  
U. V. Ramudu ◽  
R. Chandrasekar ◽  
J. Dontabhaktuni ◽  
...  
Keyword(s):  
Experimental Study ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Single Crystal ◽  
Nematic Liquid Crystal ◽  
Self Assembly ◽  
Nematic Liquid Crystals ◽  
Directed Assembly ◽  
Orientation Interaction ◽  
Organic Single Crystal

In this paper we report first experimental study on the orientation, interaction and directed-assembly of single crystal micro-sheets in nematic liquid crystals.

scholarly journals The Cauchy Problem for the Incompressible 2D-MHD with Power Law-Type Nonlinear Viscous Fluid

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Power Law ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Fluid Flows ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We investigate a motion of the incompressible 2D-MHD with power law-type nonlinear viscous fluid. In this paper, we establish the global existence and uniqueness of a weak solution u , b depending on a number q in ℝ 2 . Moreover, the energy norm of the weak solutions to the fluid flows has decay rate 1 + t − 1 / 2 .

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