Global existence of solutions of the simplified Ericksen–Leslie system in dimension two

Abstract

In the 1960s, Ericksen and Leslie established the hydrodynamic theory for modelling liquid crystal flow. In this paper, we investigate a simplified model of the Ericksen–Leslie system, which is a system of the Navier–Stokes equations coupled with the harmonic map flow. We prove global existence of solutions to the Ericksen–Leslie system in \({\mathbb{R}^{2}}\) with initial data, where the solutions are regular except for at a finite number of singular times.