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Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System

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Abstract

We study a complex non-Newtonian fluid that models the flowof nematic liquid crystals. The fluid is described by a system that couples a forced Navier–Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three.We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use cancellations that allow its existence to prove higher global regularity in dimension two. We also show the weak–strong uniqueness in dimension two.

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Authors and Affiliations

  1. Université Bordeaux 1, IMB, 33405, Talence Cedex, France

    Marius Paicu

  2. Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB, UK

    Arghir Zarnescu

Authors
  1. Marius Paicu
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  2. Arghir Zarnescu
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Correspondence to Arghir Zarnescu.

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Communicated by F. Lin

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Paicu, M., Zarnescu, A. Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System. Arch Rational Mech Anal 203, 45–67 (2012). https://doi.org/10.1007/s00205-011-0443-x

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  • DOI: https://doi.org/10.1007/s00205-011-0443-x

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