Appears in collection : Partial Differential Equations, Analysis and Geometry

We are interested in the question of mean-field limits, or deriving effective evolution equations of PDE type for a system of N points in singular interaction, for instance of Coulomb or Riesz nature, evolving by first order dynamics. We will discuss two methods: the modulated energy method, that works well for gradient flows or conservative flows of Coulomb/Riesz type energies, and a new method based on a multiscale mollification metric, which works well for up to Coulomb interaction singularity, without much structure assumed.