Logarithmically improved BKM’s criterion for the 3D nematic liquid crystal flows

This paper proves a logarithmically improved Beale–Kato–Majda’s criterion for the 3D nematic liquid crystal flows, which says that if ∫0T‖∇×u(t,⋅)‖BMOln(e+‖∇×u(t,⋅)‖BMO)dt<∞, then the solution (u,d)(u,d) is smooth up to the time t=Tt=T.