Title: Stationary shear flows of nematic liquid crystals
Abstract: Nematic material is the simplest liquid crystals but provides extremely rich dynamics due to multiple parameters involved to characterize the basic local properties. The Ericksen-Leslie model of the nematic liquid crystals includes Frank's parameters for Oseen-Frank energy of crystal property and Leslie's dynamic parameters of liquid characteristics. In this talk, the focus will be on stationary solutions of simple planar shear flow of nematic liquid crystals. Even in this simplest setting, the dynamics supported by the material exhibit quick rich behavior. In applying dynamical system theory, we are able to provide a rather complete picture about the possible solutions. In particular, we are able to show existence of multiple solutions in many situations. The talk is based on a joint work with Jia Jiao and Kaiyin Huang.