Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 149-172.

A survey of results and open problems for the hydrodynamic flow of nematic liquid crystals

Jay Lawrence Hineman

Abstract:
The mathematical study of the hydrodynamic flow of nematic liquid crystals is a mix of material science, Navier-Stokes theory, and the study of harmonic maps. In this article, the basic model for the hydrodynamic flow of nematic liquid crystals is presented - that is, the Ericksen-Leslie equations. There are a number of simplifications of the Ericksen-Leslie equations exist in the literature. We give a short survey of the known mathematical results for the Ericksen-Leslie equations and its simplifications. Along the way, open problems in analysis and computation for the Ericksen-Leslie system are discussed.

Published February 10, 2014.
Math Subject Classifications: 76A15, 58E20.
Key Words: Liquid crystals; Ericksen-Leslie; harmonic maps.

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