Open AccessA regularity criterion for liquid crystal flows in terms of the component of velocity and the horizontal derivative components of orientation field
Author(s) -
Qiang Li,
AUTHOR_ID,
Baoquan Yuan,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022231
Subject(s) - nabla symbol , omega , orientation (vector space) , component (thermodynamics) , field (mathematics) , physics , vorticity , liquid crystal , crystal (programming language) , derivative (finance) , combinatorics , mathematics , geometry , mathematical physics , mathematical analysis , pure mathematics , condensed matter physics , vortex , quantum mechanics , thermodynamics , computer science , financial economics , economics , programming language
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 \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<\infty,\nonumber \\ with\ \ 3< p\leq\infty,\ \frac{3}{2}< q\leq\infty,\ 3< a\leq\infty. \end{eqnarray*} $\end{document}