On the hydrodynamics of biaxial nematic liquid crystals. I: General theory
type: Item
instance of: scholarly article
title: On the hydrodynamics of biaxial nematic liquid crystals. I: General theory
zbMATH Open document ID: 0770.76005
DOI: 10.1007/BF01636993
author: Ernest H. MacMillan
published in: Archive for Rational Mechanics and Analysis
publication date: 1992-09-26T00:00:00Z
review text: The author examines the dynamics of the relaxation equation for order tensors that are near a biaxial equilibrium set when a steady, affine, isochoric fluid flow is imposed upon the fluid. The major simplification introduced here is to ignore boundary constraints on the order tensor and thus consider solutions to the equations for a fluid that fills all of space. Because of this simplification, the governing equations are ordinary differential equations. The main results of this paper are a natural kinematical description of the relaxation equation and an analysis of the parametric and linearized stability of steady-state order tensors when a flow with sufficiently small velocity gradient is imposed. The mathematical structure of the theory in this paper is a part of the general topic of bifurcation and stability theory of ordinary differential equations in the presence of a group of symmetry transformations. However, the work is not a subset of the current research activity in this field --- it provides concrete examples of the local bifurcation and stability theory near equilibria of varying dimension for a differential equation perturbed by a parameter with a variety of different symmetry types.
Mathematics Subject Classification ID: 76A15
zbMATH DE Number: 55929
zbMATH Keywords: relaxation equation
zbMATH Keywords: order tensors
zbMATH Keywords: equilibrium
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: group of symmetry transformations
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01636993
OpenAlex ID: W2069677126
description: scientific article; zbMATH DE number 55929