Existence of weak solutions to the Ericksen-Leslie model for a general class of free energies

TL;DR

This paper proves the global existence of weak solutions for a quasistatic liquid crystal model with a broad class of free energies, allowing nonlinear principal operators in the director equation.

Contribution

It introduces a novel approach to establish weak solutions for the Ericksen-Leslie model with nonlinear principal parts in the director equation.

Findings

Global existence of weak solutions is established.

The model accommodates a general class of free energies.

The principal part of the differential operator can be nonlinear.

Abstract

A quasistatic model due to Ericksen and Leslie describing incompressible liquid crystals is studied for a general class of free energies. Global existence of weak solutions is proven via a Galerkin approximation with eigenfunctions of a strongly elliptic operator. A novelty is that the principal part of the differential operator appearing in the director equation can be nonlinear.