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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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Funding

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

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Correspondence to Soojung Kim.

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The authors declare that they have no conflict of interest.

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Communicated by N. Masmoudi

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Chen, Y., Kim, S. & Yu, Y. Twisted Solutions to a Simplified Ericksen–Leslie Equation. Arch Rational Mech Anal 232, 303–336 (2019). https://doi.org/10.1007/s00205-018-1321-6

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  • DOI: https://doi.org/10.1007/s00205-018-1321-6

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