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

TL;DR

This paper proves the weak-strong uniqueness principle for Euler-Poisson systems using Riesz potentials to justify weak formulations and employing relative energy methods.

Contribution

It introduces a novel application of Riesz potentials to handle Poisson's equation within the weak-strong uniqueness framework for Euler-Poisson systems.

Findings

Weak-strong uniqueness is established for the Euler-Poisson system.

Riesz potentials are effectively used to justify weak formulations.

The relative energy method is successfully applied in this context.

Abstract

In this article, the weak-strong uniqueness principle is proved for an Euler-Poisson system in the whole space, with initial data so that the strong solution exists. 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.