Empirical Measures and Vlasov Hierarchies - École polytechnique Access content directly
Journal Articles Kinetic and Related Models Year : 2013

Empirical Measures and Vlasov Hierarchies


The present note reviews some aspects of the mean field limit for Vlasov type equations with Lipschitz continuous interaction kernel. We discuss in particular the connection between the approach involving the N-particle empirical measure and the formulation based on the BBGKY hierarchy. This leads to a more direct proof of the quantitative estimates on the propagation of chaos obtained on a more general class of interacting systems in [S. Mischler, C. Mouhot, B. Wennberg, arXiv:1101.4727]. Our main result is a stability estimate on the BBGKY hierarchy uniform in the number of particles, which implies a stability estimate in the sense of the Monge-Kantorovich distance with exponent 1 on the infinite mean field hierarchy. This last result amplifies Spohn's uniqueness theorem [H. Spohn, Math. Meth. Appl. Sci. 3 (1981), 445-455].
Fichier principal
Vignette du fichier
MF4.pdf (261.25 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00856485 , version 1 (01-09-2013)
hal-00856485 , version 2 (16-09-2013)



François Golse, Clément Mouhot, Valeria Ricci. Empirical Measures and Vlasov Hierarchies. Kinetic and Related Models , 2013, 6 (2013), pp.919-943. ⟨10.3934/krm.2013.6.919⟩. ⟨hal-00856485v2⟩
414 View
421 Download



Gmail Facebook X LinkedIn More