Global existence of solutions of the Liquid Crystal flow for the Oseen-Frank model

Details Global existence of solutions of the Liquid Crystal flow for the Oseen-Frank model Global existence of solutions of the Liquid Crystal flow for the Oseen-Frank model

2010-10-20

arxiv.org/abs/1010.4083v1

Mathematics

Analysis of PDEs

39 pages

Scientific paper

In the first part of this paper, we establish global existence of solutions of the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The liquid crystal flow is a prototype of equations from the Ericksen-Leslie system in the hydrodynamic theory and generalizes the heat flow for harmonic maps into the 2-sphere. The Ericksen-Leslie system is a system of the Navier-Stokes equations coupled with the liquid crystal flow. In the second part of this paper, we also prove global existence of solutions of the Ericksen-Leslie system for a general Oseen-Frank model in $\Bbb R^2$.

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