N-particles approximation of the Vlasov equations with singular potential

Hauray, Maxime; Jabin, Pierre-Emmanuel

Hauray, Maxime; Jabin, Pierre-Emmanuel (2007), N-particles approximation of the Vlasov equations with singular potential, Archive for Rational Mechanics and Analysis, 183, 3, p. 489-524. http://dx.doi.org/10.1007/s00205-006-0021-9

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00000670/en/

Date

2007

Journal name

Archive for Rational Mechanics and Analysis

Volume

183

Number

Publisher

Springer

Pages

489-524

Abstract (FR)

On démontre la convergence pour tout temps d'une approximation de l'equation de Vlasov par un système de particules sans régularisation du champ, ceci pour des potentiels singuliers, avec une force du type $1/|x|^{\alpha}$, pour \alpha plus petit que 1.

Abstract (EN)

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.

Subjects / Keywords

Dérivation d'équations cinétiques; système de particules; Equation de Vlasov