Analysis of 1+1 Dimensional Stochastic Models of Liquid Crystal Polymer Flows∗

We consider the stochastic model of concentrated Liquid Crystal Polymers(LCPs) in the plane Couette flow. The dynamic equation for the liquid crystal polymers is described by a nonlinear stochastic differential equation with Maier-Saupe interaction potential. The stress tensor is obtained from an ensemble average of microscopic polymer configurations. We present the local existence and uniqueness theorem for the solution of the coupled fluid-polymer system. We also analyze the error of a fully finite difference-Monte Carlo hybrid numerical scheme by investigating the asymptotic behavior of weakly interacting processes. It is proved that the rate of convergence of the full discretized scheme is O(h2 + δt + 1 √ M ).