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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| Jay Lawrence Hineman Department of Mathematics, University of Kentucky Lexington, KY 40506, USA email: jay.hineman@uky.edu |
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