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



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)

35B40 35B41 35Q35 76D05 


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghaiChina
  2. 2.Department of MathematicsPenn State UniversityState CollegeUSA

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