(untitled) (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.