Young Measures and Order-Disorder Transition in Stationary Flow of Liquid Crystals

We study a system of nonlinear second order ordinary differential equations modeling Poiseuille flow of liquid crystals with variable degree of orientation, at the limit of large Ericksen number. The system is singularly perturbed and degenerate, and as a result the solutions are highly oscillatory. We obtain the relations satisfied by the Young measures generated by sequences of weak solutions, and show that the persistent oscillations are encoded in the Young measure generated by the molecular alignment variable. The effective equations correspond to the macroscopic isotropic Newtonian flow with a liquid crystalline microstructure indicating a remnant alignment.