Archive for Rational Mechanics and Analysis

, Volume 183, Issue 3, pp 489–524

N-particles Approximation of the Vlasov Equations with Singular Potential

Article

DOI: 10.1007/s00205-006-0021-9

Cite this article as:
Hauray, M. & Jabin, P. Arch Rational Mech Anal (2007) 183: 489. doi:10.1007/s00205-006-0021-9

Abstract

We prove the convergence in any time interval of a point-particle approximation of the Vlasov equation by particles initially equally separated for a force in 1/|x|α, with \(\alpha \leqq 1\). We introduce discrete versions of the L norm and time averages of the force-field. The core of the proof is to show that these quantities are bounded and that consequently the minimal distance between particles in the phase space is bounded from below.

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, U.M.R. no 7598 du C.N.R.S.Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Laboratoire J.-A. Dieudonn, U.M.R. no 6621 du C.N.R.S.Université de Nice – Sophia Antipolis Parc ValroseNice Cedex 02France