Stability of shear flows of polymeric liquid crystals

This article deals with flow phenomena in liquid crystal materials. The governing equations are a generalization of the Leslie-Ericksen equations for liquid crystals with variable degree of orientation. The goal of the analysis is to study the role of the order parameter in the model. We examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyze their stability under physically realistic conditions (such conditions turn out to be compatible with the high viscosities of polymeric materials). In particular, we observe that ellipticity of the linearized system of governing equations is a consequence of the Clausius-Duhem inequality.