Weak-strong uniqueness and high-friction limit for Euler-Riesz systems

TL;DR

This paper proves a weak-strong uniqueness principle and high-friction limit convergence for Euler-Riesz systems using the relative energy method, addressing technical challenges with a Hardy-Littlewood-Sobolev inequality.

Contribution

It introduces a novel application of the relative energy method to Euler-Riesz systems and establishes convergence in the high-friction limit.

Findings

Weak-strong uniqueness principle established

Convergence towards a gradient flow in high-friction limit demonstrated

Technical innovation with Hardy-Littlewood-Sobolev inequality for Riesz potentials

Abstract

In this work we employ the relative energy method to obtain a weak-strong uniqueness principle for a Euler-Riesz system, as well as to establish its convergence in the high-friction limit towards a gradient flow equation. The main technical challenge in our analysis is addressed using a specific case of a Hardy-Littlewood-Sobolev inequality for Riesz potentials.