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

The role of Riesz potentials in the weak-strong uniqueness for the Euler-Poisson system

“…The weak-strong uniqueness principle has also been studied for the Euler-Poisson system with linear damping and confinement in a bounded smooth domain, for classes of measure-valued solutions; in this case being called measure-valued-strong uniqueness [3]. Furthermore, it has as well been studied for a similar set of equations, the Navier-Stokes-Poisson system, for classes of weak solutions that are continuous in time with respect to the weak topology [2]. In those cases, the relative energy method was employed to achieve a stability estimate from which the weak-strong uniqueness follows.…”