Anisotropic nematic liquid crystals in an applied magnetic field

Abstract

In the paper, we study the effect of an applied magnetic field on nematic liquid crystals such as magnetic field-induced instability in anisotropic liquid crystals. Under a planar field ansatz for the liquid crystal, the time-dependent system of anisotropic liquid crystals for the Oseen–Frank model reduces to a quasilinear parabolic equation for the orientation angle of the liquid crystal involving critical nonlinearity due to elastic anisotropy. We first establish the global existence of weak solutions to the parabolic problem. When the unequal elastic constants are sufficiently close, we prove convergence to an equilibrium of global smooth solutions, and examine the dynamical instability of an aligned state induced by a strong magnetic field.