Singular flows with time-varying weights
Analysis of PDEs
2025-03-06 v2
Abstract
We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty \cite{duerinckx2020mean} and Bresch-Jabin-Wang \cite{bresch2019modulated}, which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of \cite{duerinckx2020mean,bresch2019modulated}, as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proved.
Cite
@article{arxiv.2503.02276,
title = {Singular flows with time-varying weights},
author = {Immanuel Ben Porat and José A. Carrillo and Pierre-Emmanuel Jabin},
journal= {arXiv preprint arXiv:2503.02276},
year = {2025}
}
Comments
46 pages