On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability
Abstract
In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed.
Keywords
Cite
@article{arxiv.1105.2180,
title = {On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability},
author = {Hao Wu and Xiang Xu and Chun Liu},
journal= {arXiv preprint arXiv:1105.2180},
year = {2013}
}