Weak-strong uniqueness for compressible Navier-Stokes system with slip boundary conditions on time dependent domains

TL;DR

This paper proves the weak-strong uniqueness property for the compressible Navier-Stokes equations with slip boundary conditions on moving domains, using a relative entropy method adapted to time-dependent geometries.

Contribution

It extends the weak-strong uniqueness framework to compressible flows on moving domains with slip boundary conditions, incorporating a novel relative entropy inequality.

Findings

Established weak-strong uniqueness for the system

Derived a relative entropy inequality on moving domains

Validated the approach for slip boundary conditions

Abstract

We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of Feireisl et al. for the system on moving domain and use it to prove the weak-strong uniqueness property.