scholarly journals Regularity Criterion for the Nematic Liquid Crystal Flows in Terms of Velocity

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Ruiying Wei ◽  
Zheng-an Yao ◽  
Yin Li
Keyword(s):  
Liquid Crystal ◽  
Fractional Derivative ◽  
Nematic Liquid Crystal ◽  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Regularity Criterion ◽  
Nematic Liquid Crystal Flows

We study the regularity criterion for the 3D nematic liquid crystal flows in the framework of anisotropic Lebesgue space. More precisely, we proved some sufficient conditions in terms of velocity or the fractional derivative of velocity in one direction.

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.

scholarly journals A regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field

2021 ◽  
Vol 7 (3) ◽  
pp. 4168-4175
Author(s):  
Qiang Li ◽  
◽  
Baoquan Yuan ◽  
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Velocity Component ◽  
Smooth Solution ◽  
Regularity Criterion ◽  
Orientation Field ◽  
Horizontal Derivative ◽  
Nematic Liquid Crystal Flows ◽  
Vorticity Component

<abstract><p>In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution $ (u, d) $ is regular provided that velocity component $ u_{3} $, vorticity component $ \omega_{3} $ and the horizontal derivative components of the orientation field $ \nabla_{h}d $ satisfy</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \int_{0}^{T}|| u_{3}||_{L^{p}}^{\frac{2p}{p-3}}+||\omega_{3}||_{L^{q}}^{\frac{2q}{2q-3}}+||\nabla_{h} d||_{L^{a}}^{\frac{2a}{a-3}} \mbox{d} t&lt;\infty,\nonumber \\ with\ \ 3&lt; p\leq\infty,\ \frac{3}{2}&lt; q\leq\infty,\ 3&lt; a\leq\infty. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> </abstract>

scholarly journals A Regularity Criterion for Compressible Nematic Liquid Crystal Flows

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jishan Fan ◽  
Tohru Ozawa
Keyword(s):  
Liquid Crystal ◽  
Bounded Domain ◽  
Nematic Liquid Crystal ◽  
Blow Up ◽  
Strong Solutions ◽  
Regularity Criterion ◽  
Flow Modeling ◽  
Nematic Liquid Crystal Flows ◽  
Local Strong Solutions ◽  
Compressible Nematic Liquid Crystal

We prove a blow-up criterion for local strong solutions to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in a bounded domain.

A new regularity criterion for the nematic liquid crystal flows

2012 ◽  
Vol 91 (9) ◽  
pp. 1741-1747 ◽  
Author(s):  
Sadek Gala ◽  
Qiao Liu ◽  
Maria Alessandra Ragusa
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Regularity Criterion ◽  
Nematic Liquid Crystal Flows
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