Weak-Strong Uniqueness for the Isentropic Euler Equations with Possible Vacuum

TL;DR

This paper proves that for the isentropic Euler equations, any energy-admissible weak solution with the same initial data matches a sufficiently regular strong solution, even if vacuum regions are present in the strong solution.

Contribution

It establishes a weak-strong uniqueness result for the isentropic Euler equations allowing for vacuum in the strong solution, extending previous results.

Findings

Weak-strong uniqueness holds even with vacuum regions.

Weak solutions coincide with strong solutions under the given conditions.

The result broadens the applicability of uniqueness principles in fluid dynamics.

Abstract

We establish a weak-strong uniqueness result for the isentropic compressible Euler equations, that is: As long as a sufficiently regular solution exists, all energy-admissible weak solutions with the same initial data coincide with it. The main novelty in this contribution, compared to previous literature, is that we allow for possible vacuum in the strong solution.