A duality method for mean-field limits with singular interactions
Analysis of PDEs
2025-02-12 v2 Mathematical Physics
math.MP
Abstract
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. In case of first-order systems, it allows to recover in particular the mean-field limit to the 2d Euler and Navier-Stokes equations. The approach also provides convergence rates.
Cite
@article{arxiv.2402.04695,
title = {A duality method for mean-field limits with singular interactions},
author = {Didier Bresch and Mitia Duerinckx and Pierre-Emmanuel Jabin},
journal= {arXiv preprint arXiv:2402.04695},
year = {2025}
}
Comments
44 pages