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