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Carnegie Mellon Center for Nonlinear Analysis
Regularity of Solutions to the Liquid Crystals Systems in $ \mathbb{R}^2$ and $ \mathbb{R}^3$

 

Mimi Dai
University of California, Santa Cruz
Department of Mathematics
mdai@slugmail.ucsc.edu


Abstract: The global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by other authors. In our paper we study the regularity and uniqueness of solutions for to systems of nematic liquid crystals. We establish that, in $ \mathbb{R}^2$, the global regularity with general data; in $ \mathbb{R}^3$, the global regularity with small initial data and a local (short time) regularity with large data. In addition, with more smoothness assumption on initial data, we obtain the uniqueness both for dimension 2 and 3 cases.