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

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 R(2) with initial data, where the solutions are regular except for at a finite number of singular times.