Logarithmically improved regularity criterion for the nematic liquid crystal flows in (B) over dot∞,∞-1 space

In this work, we study the regularity criterion of the three-dimensional nematic liquid crystal flows. It is proved that if the vorticity satisfies integral(T)(0) parallel to omega(t, .)parallel to(2)((B) over dot infinity,infinity-1)/1 + log(e + parallel to omega(t, .)parallel to((B) over dot infinity,infinity-1))dt