Small inertia limit for coupled kinetic swarming models

2024/02/05 by Young-Pil Choi, Choi, Young-Pil, Simone Fagioli +3 · 2 citations
Mathematics · Physics and Astronomy · #35A01 #35A21 #35Q70 #82C40 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2402.02854

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate various versions of multi-dimensional systems involving many species, modeling aggregation phenomena through nonlocal interaction terms. We establish a rigorous connection between kinetic and macroscopic descriptions by considering the small-inertia limit at the kinetic level. The results are proven either under smoothness assumptions on all interaction kernels or under singular assumptions for self-interaction potentials. Utilizing different techniques in the two cases, we demonstrate the existence of a solution to the kinetic system, provide uniform estimates with respect to the inertia parameter, and show convergence towards the corresponding macroscopic system as the inertia approaches zero.

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• Cross-diffusion limits in multispecies kinetic models
• Micro-macro and macro-macro limits for controlled leader-follower systems

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