On liquid crystal flows with free-slip boundary conditions

Chun Liu; Jie Shen

doi:10.3934/dcds.2001.7.307

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2001, Volume 7, Issue 2: 307-318. Doi: 10.3934/dcds.2001.7.307

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On liquid crystal flows with free-slip boundary conditions

Chun Liu^1, and
Jie Shen²

1.
Department of Mathematics and Center for Materials Physics, Penn State University, University Park, PA 16802
2.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Revised: September 30, 2000

Published: March 2000

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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.

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Mathematics Subject Classification: 35K60, 76D03, 76D05.

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