Long time behavior and field-induced instabilities of smectic liquid crystals

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In this paper, we study long time behavior and dynamical instabilities of smectic liquid crystals in an applied magnetic field. Under a planar ansatz of the de Gennes model, we first establish existence of global weak solutions and prove convergence to an equilibrium as t tends to infinity. Then we discuss field-induced dynamical instability of pure smectic states and dynamical instability of the pure nematic states, which rely on weak instabilities of the pure smectic and nematic states in magnetic fields.