The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell

TL;DR

This paper models the interaction of a 2D nematic liquid crystal with a 1D flexible shell, proving the existence of global weak solutions and their convergence as the Ginzburg-Landau parameter varies.

Contribution

It introduces a coupled macroscopic model of liquid crystal and flexible shell, establishing global weak solutions and their convergence without the Ginzburg-Landau approximation.

Findings

Constructed global weak solutions for the coupled system.

Proved convergence of solutions as the Ginzburg-Landau parameter tends to zero.

Extended the understanding of liquid crystal-shell interactions.

Abstract

We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is modelled by the simplified Ericksen-Leslie system with Ginzburg-Landau approximation. The liquid crystal is contained in a thin viscoelastic shell of arbitrary reference configuration that evolves with respect to the forces exerted by the liquid crystal. Barring any degeneracies in the shell, we construct a global weak solution for the coupled system. We then show that any family of such weak solutions that are parametrized by the Ginzburg-Landau coefficient, converges to a weak solution of the original simplified Ericksen-Leslie system without the Ginzburg-Landau term.