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

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(ϱ)=aϱ^γ and allowing the density to be close or equal to zero. In particular, the result will be first obtained for an adiabatic exponent γ∈[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.