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

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.

References in corpus (3)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Nonstationary models for liquid crystals: A fresh mathematical perspective
• Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions

Cited by in corpus (5)

• Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank free energy
• Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy
• Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system
• Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
• Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations