## Communications in Mathematical Sciences

### Long Time Behavior of Particle Systems in the Mean Field Limit

#### Abstract

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.

#### Article information

Source
Commun. Math. Sci., Volume 5 (2007), 11-19.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.cms/1175797794

Mathematical Reviews number (MathSciNet)
MR2301286

Zentralblatt MATH identifier
1138.82342

#### Citation

Caglioti, Emanuele; Rousset, Frédéric. Long Time Behavior of Particle Systems in the Mean Field Limit. Commun. Math. Sci. 5 (2007), 11--19. https://projecteuclid.org/euclid.cms/1175797794