In this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

中文翻译：

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具有各向异性能量和外力的二维Ericksen-Leslie方程

在本文中，我们考虑了二维Ericksen-Leslie方程，该方程描述了向列液晶在外部力作用下的流体动力学，以及各向异性能量对应用的外部控制能量（例如磁场或电场）进行建模。在关于初始数据，外部数据和各向异性能量的一般假设下，我们证明了有限次奇异时间全局弱解的存在性和唯一性。如果初始数据和外力足够小，则我们可以确定整体弱解不具有任何奇异时间，并且只要数据是规则的就可以确定。