On the General Ericksen-Leslie System: Parodi's Relation, Well-Posedness and Stability

Hao Wu, Xiang Xu, Chun Liu

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


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 μ4 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.

Original languageEnglish (US)
Pages (from-to)59-107
Number of pages49
JournalArchive for Rational Mechanics and Analysis
Issue number1
StatePublished - Apr 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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