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

Abstract

In this article, the weak-strong uniqueness principle is proved for the Euler-Poisson system in the whole space, with initial data so that the strong solution exists, and allowing for the density to assume vacuum states. Some results on Riesz potentials are used to justify the considered weak formulation. Then, one follows the relative energy methodology and, in order to handle the solution of Poisson's equation, employs the theory of Riesz potentials.