论文标题
关于Ericksen-Leslie系统的奇异性
On singularities of Ericksen-Leslie system in dimension three
论文作者
论文摘要
在本文中，我们考虑了Ericksen-Leslie系统的初始和边界价值问题，该系统模拟了三个尺寸的nematic液晶流。在有限时间构建了两个奇点的例子。第一个示例是在特殊的轴对称类中构建的，具有合适的轴对称初始数据和边界数据，而第二个示例是为具有较小能量但非平凡拓扑的初始数据构建的。系统的最大原理的反面示例是通过利用尺寸的Poiseuille流量来构建的。
In this paper, we consider the initial and boundary value problem of Ericksen-Leslie system modeling nematic liquid crystal flows in dimension three. Two examples of singularity at finite time are constructed. The first example is constructed in a special axisymmetric class with suitable axisymmetric initial and boundary data, while the second example is constructed for an initial data with small energy but nontrivial topology. A counter example of maximum principle to the system is constructed by utilizing the Poiseuille flow in dimension one.
