TY - JOUR
T1 - Liquid Crystal Flows with Regularity in One Direction
AU - Zhang , Zujin
JO - Journal of Partial Differential Equations
VL - 3
SP - 245
EP - 250
PY - 2014
DA - 2014/09
SN - 27
DO - http://doi.org/10.4208/jpde.v27.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/5140.html
KW - Liquid crystals
KW - regularity criteria
AB -  In this paper, we consider the Cauchy problem for the model of liquid crystal. We show that if the velocity field u satisfies $$∂_3u∈L^p(0,T;L^q(\mathbb{R}^3)), \frac{2}{p}+\frac{3}{q}+=1+\frac{1}{q}, 2 ‹ q ≤ ∞,$$ then the solution is in fact smooth.