High-friction limit for bipolar Euler-Riesz systems

2025/09/06 by Nuno J. Alves, Alves, Nuno J., Jan Haškovec +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Brake Systems and Friction Analysis #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2509.05742

openalex publication_date 2025/09/06 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/29

Abstract

We consider a bipolar Euler-Riesz system and rigorously justify the high-friction limit of weak solutions towards a bipolar aggregation-diffusion system with Riesz interactions. The analysis is carried out via the relative entropy method in the regime where smooth solutions of the limiting equations exist. This extends previous results on the high-friction limit of bipolar Euler-Poisson systems to a more general class of interactions, and extends the one-species Euler-Riesz case to the bipolar setting.

Citations

• Global Existence and Nonlinear Stability of Finite-Energy Solutions of the Compressible Euler-Riesz Equations with Large Initial Data of Spherical Symmetry
• A bilinear fractional integral operator for Euler-Riesz systems
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• The Euler-Maxwell two-fluid system in 3D
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• Large friction-high force fields limit for the nonlinear Vlasov--Poisson--Fokker--Planck system
• Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations