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 \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.