Regularity and long time behavior of solutions to the nematic Liquid Crystal Systems
Abstract: We consider the Ericksen-Leslie model for nematic liquid crystal (LCD) systems. Regularity and uniqueness of solutions to the density dependent LCD system were established. In two dimension, global regular solutions exist with general data; in three dimension, global regular solutions exist with the assumption of small initial data and short time regular solutions exist for large data. In addition, with more smoothness assumption on initial data, we obtain the uniqueness both for dimension 2 and 3 cases. Furthermore, in the case of constant density, the long time behavior of regular solutions was studied and optimal decay (time) rate was obtained for the solutions in all of the Sobolev spaces $H^m$ with $m \geq 0$.
Friday September 13, 2013 at 3:00 PM in SEO 636