Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions

Abstract

We study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept, often applied in the context of compressible Euler- or related systems of fluid dynamics, to prove weak-strong uniqueness of solutions. A main novelty is that the relative energy inequality is proved for a system with a nonconvex energy.

References in corpus (3)

• Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank free energy
• Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy
• Weak-strong uniqueness property for the compressible flow of liquid crystals

Cited by in corpus (2)

• Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
• Existence of weak solutions to the Ericksen-Leslie model for a general class of free energies