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Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows. (English) Zbl 1185.35178

Summary: 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 by using the Łojasiewicz-Simon approach. Moreover, we provide an estimate on the convergence rate.

MSC:

35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
76D05 Navier-Stokes equations for incompressible viscous fluids
35N20 Overdetermined initial value problems for PDEs and systems of PDEs
76A15 Liquid crystals
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