American Institute of Mathematical Sciences

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

 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.
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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