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On the long-time behavior of some mathematical models for nematic liquid crystals

  • Hana Petzeltová
  • Elisabetta RoccaEmail author
  • Giulio Schimperna
Article

Abstract

A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the velocity field u and the director field d, representing the preferred orientation of molecules in a neighborhood of any point in a reference domain. After recalling a known existence result, we investigate the long-time behavior of weak solutions. In particular, we show that any solution trajectory admits a non-empty ω-limit set containing only stationary solutions. Moreover, we give a number of sufficient conditions in order that the ω-limit set contains a single point. Our approach improves and generalizes existing results on the same problem.

Mathematics Subject Classification (2000)

35B40 35K45 76A15 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Hana Petzeltová
    • 1
  • Elisabetta Rocca
    • 2
    Email author
  • Giulio Schimperna
    • 3
  1. 1.Institute of Mathematics of the Czech Academy of SciencesPraha 1Czech Republic
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanoItaly
  3. 3.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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