Empirical measures and Vlasov hierarchies

Valeria Ricci, François Golse, Clément Mouhot

Risultato della ricerca: Articlepeer review

10 Citazioni (Scopus)

Abstract

The present note reviews some aspects of the mean eld limit forVlasov type equations with Lipschitz continuous interaction kernel. We discussin particular the connection between the approach involving the N-particleempirical measure and the formulation based on the BBGKY hierarchy. Thisleads to a more direct proof of the quantitative estimates on the propagationof 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 stabilityestimate on the BBGKY hierarchy uniform in the number of particles, whichimplies a stability estimate in the sense of the Monge-Kantorovich distancewith exponent 1 on the in nite mean eld hierarchy. This last result ampli esSpohn's uniqueness theorem [H. Spohn, Math. Meth. Appl. Sci. 3 (1981),445{455].
Lingua originaleEnglish
pagine (da-a)919-943
Numero di pagine25
RivistaKinetic and Related Models
Volume6
Stato di pubblicazionePublished - 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

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