Singularity formation for the general Poiseuille flow of nematic liquid crystals

TL;DR

This paper demonstrates the formation of finite-time cusp singularities in the Poiseuille flow of nematic liquid crystals modeled by the Ericksen-Leslie system, highlighting the impact of quasilinear wave equations.

Contribution

It constructs a new example of cusp singularity formation in nematic liquid crystal flow, extending previous results to a more general setting.

Findings

Finite-time cusp singularity can occur in nematic liquid crystal flow.

The singularity arises due to the quasilinear nature of the wave component.

Extension of earlier specific case results to a broader model.

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.