By Olivier Faugeras
Mean-Field Limits for Singular Flows
Appears in collection : Advances in Nonlinear Analysis and Nonlinear Waves, a conference in honor of Frank Merle
We consider a system of N points in singular interaction of Coulomb or Riesz type, evolving by gradient flow or conservative flow (such as the point vortex system in 2D) with or without noise. We discuss convergence to the mean-field limit by a modulated energy method, that relies on a commutator estimate. The method also allows to obtain global-in-time convergence.