On the Stability of Travelling Waves Arising in Nematic Liquid Crystals

Abstract

The stability of travelling waves which occur when a nematic liquid crystal is subjected to crossed electric and magnetic fields has been studied previously where conditions on a control parameter q for stability to occur have been given. This article is concerned with the behaviour of the stable perturbations as time increases. For each of the three travelling wave solutions we can determine the long-term monotonic or oscillatory behaviour of the perturbations using knowledge of the spectrum of the operator governing the perturbation equation.