# American Institute of Mathematical Sciences

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

## On liquid crystal flows with free-slip boundary conditions

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