Communications in Mathematical Sciences
Volume 5 (2007)
Supplemental Issue 1
Long Time Behavior of Particle Systems in the Mean Field Limit
Pages: 11 – 19
We 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 Liouville 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.
Vlasov type equations; particles systems; stability
2010 Mathematics Subject Classification