N-particles Approximation of the Vlasov Equations with Singular Potential |
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| Authors: | Maxime Hauray Pierre-Emmanuel Jabin |
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| Institution: | 1.Laboratoire Jacques-Louis Lions, U.M.R. no 7598 du C.N.R.S.,Université Pierre et Marie Curie,Paris Cedex 05,France;2.Laboratoire J.-A. Dieudonn, U.M.R. no 6621 du C.N.R.S.,Université de Nice – Sophia Antipolis Parc Valrose,Nice Cedex 02,France |
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| 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
 . 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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| Keywords: | |
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