Twisted Solutions to a Simplified Ericksen-Leslie Equation

초록

In this article we construct global solutions to a simplified Ericksen-Leslie system on R3. The constructed solutions are twisted and periodic along the x(3)-axis with period d=2/. Here >0 is the twist rate and d is the distance between two planes which are parallel to the x(1)x(2)-plane. Liquid crystal material is placed in the region enclosed by these two planes. Given a well-prepared initial data, our solutions exist classically for all t(0,). However, these solutions become singular at all points on the x(3)-axis and escape into third dimension exponentially while t. An optimal blow up rate is also obtained.