Archive for Rational Mechanics and Analysis

, Volume 232, Issue 1, pp 303–336

# Twisted Solutions to a Simplified Ericksen–Leslie Equation

Article

## Abstract

In this article we construct global solutions to a simplified Ericksen–Leslie system on $${\mathbb{R}^3}$$. The constructed solutions are twisted and periodic along the x3-axis with period $${d = 2\pi \big/ \mu}$$. Here $${\mu > 0}$$ is the twist rate and d is the distance between two planes which are parallel to the x1x2-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 $${t \in (0, \infty)}$$. However, these solutions become singular at all points on the x3-axis and escape into third dimension exponentially while $${t \rightarrow \infty}$$. An optimal blow up rate is also obtained.

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