LAUSR

We apply the Ericksen–Leslie dynamic model to investigate stationary solutions of planar shear flows for nematic liquid crystals. Nematic material is extremely rich and involves several parameters to characterize the basic local properties. The Ericksen–Leslie model of the nematic material includes Frank’s parameters for Oseen–Frank energy and Leslie’s dynamic parameters. Even in this simple setting of shear flows, the dynamics supported by the material exhibit quick rich behavior. With the aid of a Hamiltonian formulation and phase plane portraits, we are able to provide a rather complete picture about the possible solutions. In particular, we establish the existence of multiple solutions for the boundary value problem in many situations. We also try to explain the physical reasons for some of the results.