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.
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