Formation of small scales in nonlinear PDEs

Mean-Field limits for Coulomb-type dynamics

Sylvia Serfaty

New York University

We consider a system of N particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow. By Riesz interaction, we mean inverse power s of the distance with s between d-2 and d where d denotes the dimension. We present a convergence result as N tends to infinity to the expected limiting mean field evolution equation. We also discuss related results for Ginzburg-Landau vortex dynamics.