@Article{JPDE-28-4,
author = {Meng, Bai and Qiao, Liu and Zhao, Jihong},
title = {A Logarithmically Improved Blow-up Criterion for a Simplified Ericksen-Leslie System Modeling the Liquid Crystal Flows},
journal = {Journal of Partial Differential Equations},
year = {2015},
volume = {28},
number = {4},
pages = {358--369},
abstract = { 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.},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v28.n4.5},
url = {https://global-sci.com/article/88288/a-logarithmically-improved-blow-up-criterion-for-a-simplified-ericksen-leslie-system-modeling-the-liquid-crystal-flows}
}