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Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals

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Abstract

We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model. The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation. In this paper, we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation, extended from an earlier result on a special case.

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Acknowledgements

The authors are partially supported by the NSF Grant DMS-2008504. This paper is motivated by a discussion with Weishi Liu. The authors thank Weishi Liu for the helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA

    Geng Chen & Majed Sofiani

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  1. Geng Chen
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  2. Majed Sofiani
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Correspondence to Majed Sofiani.

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Chen, G., Sofiani, M. Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals. Commun. Appl. Math. Comput. 5, 1130–1147 (2023). https://doi.org/10.1007/s42967-022-00190-5

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  • DOI: https://doi.org/10.1007/s42967-022-00190-5

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