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" 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 222b^T_0 frac||u||^ frac21-r _ dotB^-r221e,221e +||2207 d||00b2_L^221e 1+1n(e+||u||_H^S+||2207 d||_H^S)dt2039221e with 0 2264 r 2039 1 and s 2265 3, then the solution (u,d) can be smoothly extended beyond the time T.", number=4, journal=Journal of Partial Differential Equations, year=2020, month=May, pages=358–369