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.
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Communicated by N. Trudinger.
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Hong, MC. Global existence of solutions of the simplified Ericksen–Leslie system in dimension two. Calc. Var. 40, 15–36 (2011). https://doi.org/10.1007/s00526-010-0331-5
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DOI: https://doi.org/10.1007/s00526-010-0331-5