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We study the general Ericksen-Leslie system with non-constant density, whichdescribes the flow of nematic liquid crystal. In particular the modelinvestigated here is associated with Parodi's relation. We prove that: in twodimension, the solutions are globally regular with general data; in threedimension, the solutions are globally regular with small initial data, or forshort time with large data. Moreover, a weak-strong type of uniqueness resultis obtained.

Existence of regular solutions to the full Liquid Crystal System