On the stability of two nematic liquid crystal configurations

Bagisa Mukherjee; Chun Liu

doi:10.3934/dcdsb.2002.2.561

Article Contents

2002, Volume 2, Issue 4: 561-574. Doi: 10.3934/dcdsb.2002.2.561

This issue Previous Article Global stability for differential equations with homogeneous nonlinearity and application to population dynamics Next Article Linear and nonlinear stability in a diffusional ecotoxicological model with time delays

On the stability of two nematic liquid crystal configurations

Bagisa Mukherjee^1, and
Chun Liu^2,

1.
Department of Mathematics, Penn State Worthington Scranton Campus, Dunmore, PA 18512
2.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received: March 31, 2001

Revised: March 31, 2002

Published: October 2002

Abstract Related Papers Cited by

Abstract

In this article we study the stability properties of two different configurations in nematic liquid crystals. One of them is the static configuration in the presence of magnetic fields. The other one is the Poiseuille flow under the model of Ericksen for liquid crystals with variable degree of orientation [E, 91]. In the first case, we show that the planar radial symmetry solution is stable with respect to the small external magnetic field. Such phenomenon illustrates the competition mechanism between the magnetic field and the strong anchoring boundary conditions. In the Poiseuille flow case, we show that the stationary configuration obtained from our previous works [C-L, 99] [C-M, 96] is stable when the velocity gradient is small.

Keywords:

Liquid crystals,
stability.

Mathematics Subject Classification: Primary: 35J20, 35J5082, 76E05.

Citation:

Article Metrics

HTML views() PDF downloads(79) Cited by(0)

On the stability of two nematic liquid crystal configurations

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On the stability of two nematic liquid crystal configurations

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content