DIFFUSIVE TRANSPORT IN TWO-DIMENSIONAL NEMATICS

Abstract. We discuss a dynamical theory for nematic liquid crystals describ-ing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational degrees of freedom. This diffusion induces a slow motion of sin-gularities of the order parameter field. Using asymptotic methods for gradient flows, we establish a relation between the Doi-Smoluchowski kinetic equation and vortex dynamics in two-dimensional systems. We also discuss moment closures for the kinetic equation and Landau-de Gennes-type free energy dis-sipation. 1. Introduction. Dynamic