TY - JOUR
T1 - The Freedericksz Transition and the Asymptotic Behavior in Nematic Liquid Crystals
AU - Aramaki , Junichi
JO - Journal of Partial Differential Equations
VL - 3
SP - 276
EP - 294
PY - 2012
DA - 2012/09
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/5187.html
KW - Freedricksz transition
KW - variational problem
KW - liquid crystals
KW - Landau-de Gennes functional
AB - <p>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.</p>