Existence of regular solutions to the full Liquid Crystal System

Abstract: We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the solutions are globally regular with general data; in three dimension, the solutions are globally regular with small initial data, or for short time with large data. Moreover, a weak-strong type of uniqueness result is obtained.