Singularity and existence to a wave system of nematic liquid crystals

TL;DR

This paper proves the global existence and singularity formation in a wave system modeling nematic liquid crystals, showing that solutions can develop gradient blowup despite viscous damping, even with small initial energy.

Contribution

It establishes the conditions under which solutions to the nematic liquid crystal wave system develop singularities, advancing understanding of their mathematical behavior.

Findings

Solutions can blow up in gradient despite viscosity.

Small initial energy does not prevent singularity formation.

Global existence is proven under certain conditions.

Abstract

In this paper, we prove the global existence and singularity formation for a wave system from modelling nematic liquid crystals in one space dimension. In our model, although the viscous damping term is included, the solution with smooth initial data still has gradient blowup in general, even when the initial energy is arbitrarily small.