Mean-field limits: from particle descriptions to macroscopic equations
Analysis of PDEs
2021-06-16 v1
Abstract
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. We crucially make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.
Cite
@article{arxiv.2007.16025,
title = {Mean-field limits: from particle descriptions to macroscopic equations},
author = {José A. Carrillo and Young-Pil Choi},
journal= {arXiv preprint arXiv:2007.16025},
year = {2021}
}