Singular flows with time-varying weights

Immanuel Ben Porat; Jos\'e A. Carrillo; Pierre-Emmanuel Jabin

Singular flows with time-varying weights

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arxiv 2503.02276 v2 pith:R2PIITV6 submitted 2025-03-04 math.AP

Immanuel Ben Porat , José A. Carrillo , Pierre-Emmanuel Jabin This is my paper · ORCID

classification math.AP

keywords weightscitesingulartimebresch2019modulatedduerinckx2020meanfieldflows

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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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