Relaxation to fractional porous medium equation from Euler--Riesz system

Abstract

We perform asymptotic analysis for the Euler--Riesz system posed in either $\mathbb{T}^d$ or $\mathbb{R}^d$ in the high-force regime and establish a quantified relaxation limit result from the Euler--Riesz system to the fractional porous medium equation. We provide a unified approach for asymptotic analysis regardless of the presence of pressure, based on the modulated energy estimates, the Wasserstein distance of order $2$, and the bounded Lipschitz distance.