@Article{JPDE-28-358, author = {Bai , MengLiu , Qiao 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 = {http://global-sci.org/intro/article_detail/jpde/5121.html} }