Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows
Analysis of PDEs
2010-11-04 v1
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 (uniqueness of asymptotic limit) by using the \L ojasiewicz--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.
Cite
@article{arxiv.0904.0390,
title = {Long-time Behavior for Nonlinear Hydrodynamic System Modeling the Nematic Liquid Crystal Flows},
author = {Hao Wu},
journal= {arXiv preprint arXiv:0904.0390},
year = {2010}
}
Comments
26 pages