Asymptotic behavior of a hydrodynamic system in the nematic liquid crystal flows
- Liu, Chun
- Wu, Hao
- Xu, Xiang
2010 Mathematics Subject Classification
- 35B40 35B41 35Q35 76D05
- Liquid crystal flows, Navier--Stokes equation, kinematic transport, uniqueness of asymptotic limit, Łojasiewicz--Simon inequality
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.