Long time behavior of particle systems in the mean field limit

International audienceWe present a review of some recent results concerning the long time behavior of particle systems in the mean field limit. In particular we will consider the Vlasov limit for a system of particles interacting via a two body potential, the case of the vortex model, and the case of the piston. In all these cases the particle system is described, in the mean field limit, by a suitable nonlinear Lionville equation. The main problem we are interested in is the comparison between the limit dynamics and the behavior of the particle system when N is large