Archive for Rational Mechanics and Analysis

, Volume 210, Issue 3, pp 773–811 | Cite as

Equivalent Theories of Liquid Crystal Dynamics

  • François Gay-Balmaz
  • Tudor S. Ratiu
  • Cesare Tronci


There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen–Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to show that the micropolar theory includes the director theory. In this paper we show that this is the case by using symmetry reduction techniques and introducing a new system that is equivalent to the Ericksen–Leslie equations and may include disclination dynamics. The resulting equations of motion are verified to be completely equivalent, although one of the two different reductions offers the possibility of accounting for orientational defects. After applying these two approaches to the ordered micropolar theory of Lhuiller and Rey, all the results are eventually extended to flowing complex fluids, such as nematic liquid crystals.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • François Gay-Balmaz
    • 1
  • Tudor S. Ratiu
    • 2
  • Cesare Tronci
    • 3
  1. 1.CNRS/Laboratoire de Météorologie DynamiqueÉcole Normale SupérieureParis Cedex 05France
  2. 2.Section de Mathématiques and Bernoulli CenterÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Department of MathematicsUniversity of SurreyGuildfordUK

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