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January  2010, 26(1): 379-396. doi: 10.3934/dcds.2010.26.379

Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows

Hao Wu 1,

1. 

School of Mathematical Sciences, Fudan University, Han Dan Road 220, 200433 Shanghai

Received  February 2009 Revised  August 2009 Published  October 2009

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.
Keywords: Navier-Stokes Equations, Łojasiewicz-Simon approach., Nematic liquid crystal flow, convergence to steady state.
Mathematics Subject Classification: Primary: 35B40, 35B41, 35Q35; Secondary: 76D0.
Citation: Hao Wu. Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows. Discrete & Continuous Dynamical Systems, 2010, 26 (1) : 379-396. doi: 10.3934/dcds.2010.26.379
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