论文标题
列液晶流具有部分自由边界
Nematic liquid crystal flow with partially free boundary
论文作者
论文摘要
我们研究了一个简化的Ericksen-Leslie系统，该系统模拟了具有部分自由边界条件的列液晶的流动。它是用于流体速度的Navier-Stokes方程与谐波图的热流量之间的耦合系统，这两个抛物线方程对于二维分析至关重要。边界条件在物理上是自然的，它们对应于Navier滑动边界条件，速度场的摩擦为零，地图的高原-Neumann类型边界条件。在本文中，我们构建了这个耦合系统的平滑解决方案，该解决方案在边界或域内的任何有限的给定点上有限的时间爆炸。
We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes equation for the fluid velocity with a transported heat flow of harmonic maps, and both of these parabolic equations are critical for analysis in two dimensions. The boundary conditions are physically natural and they correspond to the Navier slip boundary condition with zero friction for the velocity field and a Plateau-Neumann type boundary condition for the map. In this paper we construct smooth solutions of this coupled system that blow up in finite time at any finitely many given points on the boundary or in the interior of the domain.
