On partial regularity criterion for the co-rotational Beris-Edwards system modeling nematic liquid crystal flow

Abstract We study the partial regularity of suitable weak solutions to the 3d co-rotational Beris-Edwards system modeling the hydrodynamical motion of nematic liquid crystal flows with the Landau-De Gennes bulk potential, and present an improved version of the Caffarelli-Kohn-Nirenberg criterion obtained recently by Du-Hu-Wang (2020) [9] in terms of the velocity gradient only. The result yields that the velocity field plays a more important role than the Q-tensor field in the partial regularity theory of the 3d co-rotational Beris-Edwards system.