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On the stability of two nematic liquid crystal configurations
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.