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.

中文翻译：

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近晶液晶的长时间行为和场致不稳定性

在本文中，我们研究了近场液晶在外加磁场中的长时间行为和动力学不稳定性。在de Gennes模型的平面ansatz下，我们首先建立整体弱解的存在性，并证明随着t趋于无穷大，收敛到平衡。然后我们讨论了纯近晶态的场致动力学不稳定性和纯向列相态的动力学不稳定性，这取决于磁场中纯近晶态和向列相态的弱不稳定性。