A two-component nonlinear variational wave system

We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time. We prove that a special semilinear case is globally well-p...

Full description

Saved in:
Bibliographic Details
Published in:Journal of hyperbolic differential equations 2023-09, Vol.20 (3), p.603-627
Main Authors: Aursand, Peder, Nordli, Anders
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time. We prove that a special semilinear case is globally well-posed. We show that a particular long time asymptotic expansion around a constant state in a moving frame satisfies the two-component Hunter–Saxton system.
ISSN:0219-8916
1793-6993
DOI:10.1142/S0219891623500182