Singularity formation for the general Poiseuille flow of nematic liquid crystals

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.

To be published in Communications on Applied Mathematics and Computation