论文标题
在2d Ericksen-Leslie方程式上，具有各向异性和外力
On the 2D Ericksen-Leslie equations with anisotropic energy and external forces
论文作者
论文摘要
在本文中，我们考虑了2D Ericksen-Leslie方程，该方程描述了用外体力和各向异性能量建模列液液晶的流体动力学，将应用外部控制的能量（例如磁场或电场）建模。在对初始数据，外部数据和各向异性能量的一般假设下，我们证明了具有有限的奇异时间的全球弱解决方案的存在和唯一性。如果初始数据和外部力量足够小，那么我们确定全局弱解决方案没有任何奇异时间，并且只要数据是常规的。
In this paper we consider the 2D Ericksen-Leslie equations which describes 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.
