Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows

Details Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows

2009-04-02

arxiv.org/abs/0904.0390v1

Discrete Contin. Dyn. Syst. Vol. 20, 379-396 (2010)

Mathematics

Analysis of PDEs

26 pages

Scientific paper

We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single steady states as time goes to infinity (uniqueness of asymptotic limit) by using the \L ojasiewicz--Simon approach. Moreover, we provide an estimate on the convergence rate. Finally, we discuss some possible extensions of the results to certain generalized problems with changing density or free-slip boundary condition.

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