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\(N\)-particles approximation of the Vlasov equations with singular potential. (English) Zbl 1107.76066

Summary: 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 \(1/|x|^{\alpha}\), with \(\alpha \leqq 1\). We introduce discrete versions of \(L^{\infty}\) 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 phase space is bounded from below.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
45K05 Integro-partial differential equations
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