Partial regularity of a nematic liquid crystal model with kinematic transport effects

Abstract

In this paper, we will establish the global existence of a suitable weak solution to the Erickson--Leslie system modeling hydrodynamics of nematic liquid crystal flows with kinematic transports for molecules of various shapes in ${\mathbb{R}^3}$, which is smooth away from a closed set of (parabolic) Hausdorff dimension at most $\frac{15}{7}$.