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

Hao Wu

doi:10.3934/dcds.2010.26.379

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2010, Volume 26, Issue 1: 379-396. Doi: 10.3934/dcds.2010.26.379

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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: January 31, 2009

Revised: July 31, 2009

Published: February 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 35Q35; Secondary: 76D05.

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