Weak-strong uniqueness principle for compressible barotropic self-gravitating fluids

TL;DR

This paper proves the weak-strong uniqueness principle for the compressible Navier-Stokes-Poisson system in exterior domains, allowing for vacuum states and extending the range of the adiabatic exponent.

Contribution

It establishes the weak-strong uniqueness for a broad class of compressible self-gravitating fluids, including cases with vacuum and boundary effects, extending previous results.

Findings

Weak-strong uniqueness holds for $eta o 0$ in the specified system.

The range of $eta$ is extended using pressure estimates and boundary analysis.

The results apply to fluids with density close to zero, including vacuum states.

Abstract

The aim of this work is to prove the weak-strong uniqueness principle for the compressible Navier-Stokes-Poisson system on an exterior domain, with an isentropic pressure of the type $p(\varrho)=a\varrho^{\gamma}$ and allowing the density to be close or equal to zero. In particular, the result will be first obtained for an adiabatic exponent $\gamma \in [9/5,2]$ and afterwards, this range will be slightly enlarged via pressure estimates "up to the boundary", deduced relaying on boundedness of a proper singular integral operator.