Singular flows with time-varying weights
Abstract
We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty duerinckx2020mean and Bresch-Jabin-Wang bresch2019modulated, which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of 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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