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November  2002, 2(4): 561-574. doi: 10.3934/dcdsb.2002.2.561

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, United States
2. 

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

Received  April 2001 Revised  April 2002 Published  August 2002

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, 76E0.
Citation: Bagisa Mukherjee, Chun Liu. On the stability of two nematic liquid crystal configurations. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 561-574. doi: 10.3934/dcdsb.2002.2.561
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