Relaxation to Fractional Porous Medium Equation from Euler–Riesz System

We perform asymptotic analysis for the Euler–Riesz system posed in either $${\mathbb {T}}^d$$ or {R}}^d$$ high-force regime and establish a quantified relaxation limit result from to fractional porous medium equation. provide unified approach regardless of presence pressure case repulsive Riesz interactions, based on modulated energy estimates, Wasserstein distance order 2, bounded Lipschitz distance. For attractive interaction case, we consider periodic domain estimate lower bound internal handle energy.