The global Cauchy problem for the Euler-Riesz equations

2024/02/01 by Young-Pil Choi, Choi, Young-Pil, Jinwook Jung +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2402.00674

openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We completely resolve the global Cauchy problem for the multi-dimensional Euler-Riesz equations, where the interaction forcing is given by ∇ (-Δ)^-σ/2ρ for some σ∈ (0,2). We construct the global-in-time unique solution to the Euler-Riesz system in a H^s Sobolev space under a smallness assumption on the initial density and a dispersive spectral condition on the initial velocity. Moreover, we investigate the algebraic time decay of convergences for the constructed solutions. Our results cover the both attractive and repulsive cases as well as the whole regime σ∈ (0,2).

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• Generalized solution and Weak-Strong uniqueness for a barotropic Euler-Riesz system

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