Existence of regular solutions to the full Liquid Crystal System

Mimi Dai

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arXiv · 1309.0476

Existence of regular solutions to the full Liquid Crystal System

Mimi Dai

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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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Mimi Dai. 2013-09-02. Existence of regular solutions to the full Liquid Crystal System. https://arxiv.org/abs/1309.0476

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