Archive for Rational Mechanics and Analysis

, Volume 183, Issue 3, pp 489–524

N-particles Approximation of the Vlasov Equations with Singular Potential

Article

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.

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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

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