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A review of mathematical analysis of nematic and smectic-A liquid crystal models

Published online by Cambridge University Press:  07 October 2013

BLANCA CLIMENT-EZQUERRA  and
FRANCISCO GUILLÉN-GONZÁLEZ
BLANCA CLIMENT-EZQUERRA
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain emails: bcliment@us.es, guillen@us.es
FRANCISCO GUILLÉN-GONZÁLEZ
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain emails: bcliment@us.es, guillen@us.es
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Abstract

We review the mathematical analysis of some uniaxial, liquid crystal phases. Firstly, we state the models for the two different studied phases: nematic and smectic-A liquid crystals. The spatial and temporal profiles of the liquid crystal configurations will be described by means of strongly nonlinear parabolic partial differential systems, which are presented at the same time. Then we will state some results about existence, regularity, time-periodicity and stability of solutions at infinite time for both models. It is our aim to show that, although nematic and smectic-A phases have different physical properties and are modelled by different nonlinear parabolic problems, there exists a common mathematical machinery to rewrite the models and obtain analytical results.

Keywords

Liquid crystalsNematic phaseSmectic-A phaseNavier–Stokes equationsGinzburg–Landau penalizationGlobal in time solutionsTime-periodic solutionsRegularityStability
Type
A Survey in Mathematics for Industry
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 133 - 153
Copyright
Copyright © Cambridge University Press 2013 

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