Archive for Rational Mechanics and Analysis

, Volume 232, Issue 1, pp 303–336 | Cite as

Twisted Solutions to a Simplified Ericksen–Leslie Equation

  • Yuan Chen
  • Soojung KimEmail author
  • Yong Yu


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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The third author is partially supported by RGC Grants Nos. 14306414 and 409613.

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Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.School of MathematicsKorea Institute for Advanced StudySeoulKorea
  3. 3.Department of MathematicsThe Chinese University of Hong KongShatin, N.T.Hong Kong

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