Weak-strong uniqueness property for the compressible flow of liquid crystals

TL;DR

This paper proves the weak-strong uniqueness property for certain compressible liquid crystal systems using relative entropy methods, addressing boundary condition challenges with new techniques.

Contribution

It introduces novel techniques to establish weak-strong uniqueness for compressible liquid crystal flows with inhomogeneous boundary conditions.

Findings

Weak-strong uniqueness is established for two liquid crystal models.

New methods are developed to handle boundary condition complexities.

The approach advances understanding of solution stability in liquid crystal flows.

Abstract

Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular direction with inhomogeneous Dirichlet boundary condition, new techniques are introduced to build up the relative entropy inequalities.