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

TL;DR

This paper proves the global existence of weak solutions for a nematic liquid crystal flow model with kinematic transport effects, showing the solution's regularity outside a small singular set in three-dimensional space.

Contribution

It establishes the existence of weak solutions with partial regularity for a complex liquid crystal model incorporating kinematic transports, advancing mathematical understanding of such systems.

Findings

Weak solutions exist globally in time.

Solutions are smooth outside a set of Hausdorff dimension at most 15/7.

The model captures kinematic transport effects in nematic liquid crystals.

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 $\frac{15}{7}$.