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arXiv · 2503.02276

Singular flows with time-varying weights

Immanuel Ben Porat·José A. Carrillo·Pierre-Emmanuel Jabin
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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.

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Immanuel Ben Porat, José A. Carrillo, Pierre-Emmanuel Jabin. 2025-03-05. Singular flows with time-varying weights. https://arxiv.org/abs/2503.02276

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