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

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

2005-04-07

arxiv.org/abs/math/0504140v1

Mathematics

Analysis of PDEs

Scientific paper

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

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