Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system

TL;DR

This paper introduces a relative entropy framework for weak solutions of the compressible Navier-Stokes equations, establishing a weak-strong uniqueness principle and providing a new tool for analyzing solution stability.

Contribution

It develops a relative entropy concept for weak solutions and proves a weak-strong uniqueness result, advancing the understanding of solution behavior in compressible fluid dynamics.

Findings

Weak solutions satisfy a relative entropy inequality.

Weak-strong uniqueness principle is established.

Framework aids in analyzing stability of solutions.

Abstract

We introduce the notion of relative entropy for the weak solutions of the compressible Navier-Stokes system. We show that any finite energy weak solution satisfies a relative entropy inequality for any pair of sufficiently smooth test functions. As a corollary we establish weak-strong uniqueness principle for the compressible Navier-Stokes system.