# On weak (measure-valued)-strong uniqueness for compressible Navier-Stokes system with non-monotone pressure law

## TL;DR

This paper introduces a new framework for solutions to the compressible Navier-Stokes equations with non-monotone pressure laws, proving existence and a weak-strong uniqueness principle using a relative energy inequality.

## Contribution

It defines a renormalised dissipative measure-valued solution for non-monotone pressure laws and proves its existence and uniqueness properties.

## Key findings

- Existence of rDMV solutions for the system.
- Establishment of a relative energy inequality.
- Weak-strong uniqueness of solutions.

## Abstract

In this paper our goal is to define a renormalised dissipative measure--valued (rDMV) solution of compressible Navier--Stokes system for fluids with non-monotone pressure--density relation. We prove existence of rDMV solutions and establish a suitable relative energy inequality. Moreover we obtain the Weak (Measure-valued)-Strong uniqueness property of this rDMV solution with the help of relative energy inequality.