Dynamics of nematic liquid crystal flows: The quasilinear approach

Matthias Georg Hieber, Manuel Nesensohn, Jan Pruss, Katharina Schade

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Consider the (simplified) Leslie.Ericksen model for the flow of nematic liquid crystals in a bounded domain ω ⊂ ℝn for n <1. This article develops a complete dynamic theory for these equations, analyzing the system as a quasilinear parabolic evolution equation in an Lp-Lq-setting. First, the existence of a unique local strong solution is proved. This solution extends to a global strong solution, provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

Original languageEnglish
Pages (from-to)397-408
Number of pages12
JournalAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume33
Issue number2
DOIs
Publication statusPublished - 2016 Mar 1
Externally publishedYes

Keywords

  • Convergence to equilibria
  • Global solutions
  • Nematic liquid crystals
  • Quasilinear parabolic evolution equations
  • Regularity

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

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