On the hydrodynamics of biaxial nematic liquid crystals. I: General theory
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.
scientific article; zbMATH DE number 55929
scientific article