On partial regularity criterion for the co-rotational Beris-Edwards system modeling nematic liquid crystal flow

2021 ◽  
Vol 301 ◽  
pp. 300-329
Author(s):  
Qiao Liu
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Partial Regularity ◽  
System Modeling ◽  
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.

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>

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