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April  2001, 7(2): 307-318. doi: 10.3934/dcds.2001.7.307

On liquid crystal flows with free-slip boundary conditions

Chun Liu 1, and  Jie Shen 2,

1. 

Department of Mathematics and Center for Materials Physics, Penn State University, University Park, PA 16802, United States
2. 

Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States

Revised  October 2000 Published  January 2001

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, 76D0.
Citation: Chun Liu, Jie Shen. On liquid crystal flows with free-slip boundary conditions. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 307-318. doi: 10.3934/dcds.2001.7.307
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