Abstract

In this paper we study the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. Under certain conditions we prove the global existence of weak solutions in dimension two or three and the existence of global regular solutions in dimension two. We also prove the weak-strong uniqueness of the solutions, for sufficiently regular initial data.

MSC codes

  1. 35Q30
  2. 76A05
  3. 76A15

Keywords

  1. nematic liquid crystal fluids
  2. Navier–Stokes equations
  3. global wellposedness

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Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 2009 - 2049
ISSN (online): 1095-7154

History

Submitted: 14 April 2010
Accepted: 21 April 2011
Published online: 1 September 2011

MSC codes

  1. 35Q30
  2. 76A05
  3. 76A15

Keywords

  1. nematic liquid crystal fluids
  2. Navier–Stokes equations
  3. global wellposedness

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