No abstract

We consider the response of a magnetic field in the theory of liquid crystals. We treat the Landau-de Gennes functional with the strong anchoring condition which may be non-constant under a magnetic field which may also be non-constant. Such situation is more general than the works of Lin and Pan in 2007 and Aramaki in 2012. We show that there exist two critical points of intensity of the field such that one corresponds to the superheating fields of superconductors and the other one corresponds to stability. We also show that under some special conditions, strong field does not bring the pure nematic state which is very different response from superconductors.

We consider the asymptotic behavior of nematic states of liquid crystals under a specific applied external fields. We use the Landau-de Gennes energy functional with the Dirichlet boundary condition for director fields. We show that in the case of equal elastic coefficients the pure nematic states are not global minimizers when we apply a strong field. Mathematics Subject Classification: 82D30, 35A15, 58K55