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

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 Łojasiewicz--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.

preprint2009arXivOpen access
Hao Wu
math.AP
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Hao Wu

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