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Global existence of solutions of the simplified Ericksen-Leslie system in dimension two. (English) Zbl 1213.35014
In the 1960s, Ericksen and Leslie established the hydrodynamic theory for modelling liquid crystal flow. In this paper, the author investigates a simplified model of the Ericksen-Leslie system for modelling liquid crystal flow, which is a system of the Navier-Stokes equations coupled with the harmonic map flow. It is proved that the 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.

##### MSC:
 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35K45 Initial value problems for second-order parabolic systems 35K55 Nonlinear parabolic equations 35Q30 Navier-Stokes equations 76A15 Liquid crystals
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