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Uniqueness of the solution to the Vlasov-Poisson system with bounded density

G. Loeper
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Abstract

In this note, we show uniqueness of weak solutions to the Vlasov-Poisson system on the only condition that the macroscopic density $ρ$ defined by $ρ(t,x) = \int_{\Rd} f(t,x,ξ)dξ$ is bounded in $\Linf$. Our proof is based on optimal transportation.

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G. Loeper. 2005-04-07. Uniqueness of the solution to the Vlasov-Poisson system with bounded density. https://arxiv.org/abs/math/0504140

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