Calculus of Variations and Partial Differential Equations

, Volume 45, Issue 3, pp 319–345

Asymptotic behavior for a nematic liquid crystal model with different kinematic transport properties


  • Hao Wu
    • School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied MathematicsFudan University
    • Department of MathematicsPenn State University
  • Chun Liu
    • Department of MathematicsPenn State University

DOI: 10.1007/s00526-011-0460-5

Cite this article as:
Wu, H., Xu, X. & Liu, C. Calc. Var. (2012) 45: 319. doi:10.1007/s00526-011-0460-5


We study the asymptotic behavior of global classical solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier–Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases.

Mathematics Subject Classification (2000)


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© Springer-Verlag 2011