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

On the stability of two nematic liquid crystal configurations

Pages: 561 - 574, Volume 2, Issue 4, November 2002      doi:10.3934/dcdsb.2002.2.561

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Bagisa Mukherjee - Department of Mathematics, Penn State Worthington Scranton Campus, Dunmore, PA 18512, United States (email)
Chun Liu - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

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.

Received: April 2001;      Revised: April 2002;      Available Online: August 2002.