Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On liquid crystal flows with free-slip boundary conditions

Pages: 307 - 318, Volume 7, Issue 2, April 2001      doi:10.3934/dcds.2001.7.307

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Chun Liu - Department of Mathematics and Center for Materials Physics, Penn State University, University Park, PA 16802, United States (email)
Jie Shen - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: In this paper, we study a coupled dynamic system describing nematic liquid crystal flows. The system was motivated by the Ericksen-Leslie equations modeling the flow of nematic liquid crystals. The purpose of studying the simplified system is to understand the flow properties of more complicated materials, the material configurations , as well as the interactions between them. Unlike in the previous studies where the Dirichlet boundary conditions are prescribed, we consider here the free-slip boundary conditions which possess a number of distinct advantages. The results in this paper form the analytical background for the forthcoming numerical simulations of the system.

Keywords:  Navier-Stokes equations, nematic liquid crystals, free-slip boundary conditions.
Mathematics Subject Classification:  35K60, 76D03, 76D05.

Revised: October 2000;      Published: January 2001.