WIAS Preprint No. 1401, (2009)

Asymptotic behavior of a hydrodynamic system in the nematic liquid crystal flows



Authors

  • Liu, Chun
  • Wu, Hao
  • Xu, Xiang

2010 Mathematics Subject Classification

  • 35B40 35B41 35Q35 76D05

Keywords

  • Liquid crystal flows, Navier--Stokes equation, kinematic transport, uniqueness of asymptotic limit, Łojasiewicz--Simon inequality

Abstract

In this paper we study the long time behavior of the classical solutions to a hydrodynamical system modeling the flow of nematic liquid crystals. This system consists of a coupled system of Navier--Stokes equations and kinematic transport equations for the molecular orientations. By using a suitable Łojasiewicz--Simon type inequality, we prove the convergence of global solutions to single steady states as time tends to infinity. Moreover, we provide estimates for the convergence rate.

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