Communications on Applied Mathematics and Computation ›› 2023, Vol. 5 ›› Issue (3): 1130-1147.doi: 10.1007/s42967-022-00190-5

• ORIGINAL PAPER • 上一篇    下一篇

Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals

Geng Chen, Majed Sofiani   

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA
  • 收稿日期:2022-01-04 修回日期:2022-01-04 出版日期:2023-09-20 发布日期:2023-08-29
  • 通讯作者: Majed Sofiani,E-mail:sofiani@ku.edu E-mail:gengchen@ku.edu;sofiani@ku.edu
  • 基金资助:
    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.

Singularity Formation for the General Poiseuille Flow of Nematic Liquid Crystals

Geng Chen, Majed Sofiani   

  1. Department of Mathematics, University of Kansas, Lawrence, KS, 66045, USA
  • Received:2022-01-04 Revised:2022-01-04 Online:2023-09-20 Published:2023-08-29
  • Contact: Majed Sofiani,E-mail:sofiani@ku.edu E-mail:gengchen@ku.edu;sofiani@ku.edu
  • Supported by:
    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.

摘要: 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.

关键词: Liquid crystals, Cusp singularity, Quasilinear wave equation

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.

Key words: Liquid crystals, Cusp singularity, Quasilinear wave equation

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