Long Time Behavior of Particle Systems in the Mean Field Limit

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.

Keywords

Vlasov type equations, particles systems, stability

2010 Mathematics Subject Classification

82C05, 82C22

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Published 1 January 2007