On weak-strong uniqueness for the compressible Navier-Stokes system with non-monotone pressure law

TL;DR

This paper proves that weak solutions to the compressible Navier-Stokes equations with non-monotone pressure laws are unique when a strong solution exists, ensuring consistency between solution types under certain conditions.

Contribution

It establishes the weak-strong uniqueness property for the compressible Navier-Stokes system with general non-monotone pressure laws, extending previous results to more general pressure conditions.

Findings

Weak solutions coincide with strong solutions from the same initial data.

The weak-strong uniqueness holds under the existence of a strong solution.

The result applies to systems with non-monotone pressure laws.

Abstract

We show the weak-strong uniqueness property for the compressible Navier-Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.