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

2021/02/03 by Young-Pil Choi, In-Jee Jeong, Choi, Young-Pil +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2102.01817

openalex publication_date 2021/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We perform asymptotic analysis for the Euler--Riesz system posed in either \mathbbT^d or 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.

Citations

• Mean field limit for Coulomb-type flows

Cited by

• Global dynamics of damped Euler systems with exterior potentials
• High-friction limit for bipolar Euler-Riesz systems

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