Variational and Topological Methods: Theory, Applications,
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 149172.
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, NavierStokes 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 EricksenLeslie equations. There are a number of simplifications
of the EricksenLeslie equations exist in the literature.
We give a short survey of the known mathematical results for the
EricksenLeslie equations and its simplifications. Along the way,
open problems in analysis and computation for the EricksenLeslie
system are discussed.
Published February 10, 2014.
Math Subject Classifications: 76A15, 58E20.
Key Words: Liquid crystals; EricksenLeslie; harmonic maps.
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Jay Lawrence Hineman
Department of Mathematics,
University of Kentucky
Lexington, KY 40506, USA
email: jay.hineman@uky.edu

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