# Vanishing viscosity limit for the compressible Navier-Stokes system via measure-valued solutions

## TL;DR

This paper demonstrates that measure-valued solutions of the barotropic Euler system can be obtained as the vanishing viscosity limit of the compressible Navier-Stokes system, establishing convergence and uniqueness results.

## Contribution

It introduces a framework linking measure-valued solutions to the vanishing viscosity limit for the compressible Navier-Stokes equations on unbounded domains.

## Key findings

- Established measure-valued solutions as limits of Navier-Stokes with vanishing viscosity.
- Proved weak-strong uniqueness principle for these solutions.
- Achieved strong convergence to the Euler system during the lifespan of strong solutions.

## Abstract

We identify a class of measure-valued solutions of the barotropic Euler system on a general (un-bounded) spatial domain as a vanishing viscosity limit for the compressible Navier-Stokes system. Then we establish the weak (measure-valued)-strong uniqueness principle, and, as a corollary, we obtain strong convergence to the Euler system on the lifespan of the strong solution.