N-particles Approximation of the Vlasov Equations with Singular Potential
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- Hauray, M. & Jabin, P. Arch Rational Mech Anal (2007) 183: 489. doi:10.1007/s00205-006-0021-9
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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.