Damped Euler system with attractive Riesz interaction forces

TL;DR

This paper studies a damped Euler system with attractive Riesz forces, proving global well-posedness near equilibrium and exponential convergence to equilibrium over time.

Contribution

It establishes the first global existence and stability results for the damped Euler system with Riesz interactions in a periodic domain.

Findings

Global well-posedness near equilibrium

Exponential convergence to equilibrium

Analysis of large-time behavior

Abstract

We consider the barotropic Euler equations with pairwise attractive Riesz interactions and linear velocity damping in the periodic domain. We establish the global-in-time well-posedness theory for the system near an equilibrium state. We also analyze the large-time behavior of solutions showing the exponential rate of convergence toward the equilibrium state as time goes to infinity.