Small inertia limit for coupled kinetic swarming models
Analysis of PDEs
2024-02-06 v1
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 \emph{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.
Cite
@article{arxiv.2402.02854,
title = {Small inertia limit for coupled kinetic swarming models},
author = {Young-Pil Choi and Simone Fagioli and Valeria Iorio},
journal= {arXiv preprint arXiv:2402.02854},
year = {2024}
}