scholarly journals Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals

2009 ◽  
Vol 25 (3) ◽  
pp. 859-867 ◽  
Author(s):  
Jishan Fan ◽  
◽  
Tohru Ozawa ◽  
Keyword(s):  
Liquid Crystals ◽  
System Modeling ◽  
Regularity Criteria ◽  
Leslie System

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 ? ?.

Remarks on regularity criteria for the weak solutions of liquid crystals

2012 ◽  
Vol 12 (4) ◽  
pp. 801-812 ◽  
Author(s):  
Zujin Zhang ◽  
Xiaofeng Wang ◽  
Zheng-an Yao
Keyword(s):  
Liquid Crystals ◽  
Weak Solutions ◽  
Regularity Criteria

scholarly journals Global weak solutions to the stochastic Ericksen–Leslie system in dimension two

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hengrong Du ◽  
Changyou Wang
Keyword(s):  
System Modeling ◽  
Energy Estimates ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Global Weak Solutions ◽  
Tensor Fields ◽  
Ginzburg Landau ◽  
Wiener Type ◽  
Leslie System ◽  
Martingale Solutions

<p style='text-indent:20px;'>We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen–Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg–Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and then the Skorokhod compactness theorem, which is built upon uniform energy estimates.</p>

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