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

• ORIGINAL PAPER • Previous Articles     Next Articles

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.

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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