The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals (Journal of Partial Differential Equations, 2012)
We consider the stability of a specific nematic liquid crystal configuration under an applied magnetic field. We show that for some specific configuration there exist two critical values H_n and H_{sh} of applied magnetic field. When the intensity of the magnetic field is smaller than H_n, the configuration of the energy is only global minimizer, when the intensity is between H_n and H_{sh}, the configuration is not global minimizer, but is weakly stable, and when the intensity is larger than H_{sh}, the configuration is instable. Moreover, we also examine the asymptotic behavior of the global minimizer as the intensity tends to the infinity.
Keywords: Freedricksz transition; variational problem; liquid crystals; Landau-de Gennes functional