Logarithmically improved criteria for the 3D nematic liquid crystal flows in the Morrey–Campanato space

We provide a sufficient condition for the regularity of solutions to the 3D nematic liquid crystal flow in the Morrey–Campanato space. More precisely, we prove that if the velocity uu satisfies ∫0T‖u(⋅,t)‖Ṁp,3r21−r1+ln(e+‖u(⋅,t)‖L6)dt<∞with  0