TY - JOUR
T1 - A Logarithmically Improved Blow-up Criterion for a Simplified Ericksen-Leslie System Modeling the Liquid Crystal Flows
AU - Bai , Meng
AU - Liu , Qiao
AU - Zhao , Jihong
JO - Journal of Partial Differential Equations
VL - 4
SP - 358
EP - 369
PY - 2015
DA - 2015/12
SN - 28
DO - http://doi.org/10.4208/jpde.v28.n4.5
UR - https://global-sci.org/intro/article_detail/jpde/5121.html
KW - Ericksen-Leslie system
KW - Navier-Stokes equations
KW - blow-up criterion
AB -  In this paper, we prove a logarithmically improved blow-up criterion in terms of the homogeneous Besov spaces for a simplified 3D Ericksen-Leslie system modeling the hydrodynamic flow of nematic liquid crystal. The result shows that if a local smooth solution (u,d) satisfies $$∫^T_0\frac{||u||^{\frac{2}{1-r}}_{\dot{B}^{-r}{∞,∞}}+||∇ d||²_{L^∞}}{1+1n(e+||u||_H^S+||∇ d||_H^S)}dt‹∞$$ with 0 ≤ r ‹ 1 and s ≥ 3, then the solution (u,d) can be smoothly extended beyond the time T.