Approximation of Liquid Crystal Flows

Noel Walkington
Department of Mathematical Sciences
Carnegie Mellon University

Abstract: The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen-Leslie equations is considered. The system of equations considerd comprises of the Navier Stokes equations coupled to an equation describing the evolution of the director field of the liquid crystal. This work builds upon the fundamental work of Lin and Liu who established energy estimates and existance/well posedness for such systems of equations. Finite element approximations are considered, and numerical experiments exhibiting the interaction of singularities and the coupling of the director and momentum equations are presented.