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

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.

Keywords:

• Euler–Poisson system
• Riesz potentials
• weak–strong uniqueness

1991 Mathematics Subject Classifications:

• 35Q35
• 35D30
• 35D35
• 76W05

Acknowledgments

The author would like to thank Professor Athanasios Tzavaras for many helpful conversations.

Disclosure statement

No potential conflict of interest was reported by the author(s).