Uniqueness of the solution to the Vlasov-Poisson system with bounded density
arXiv:math/0504140
Abstract
In this note, we show uniqueness of weak solutions to the Vlasov-Poisson system on the only condition that the macroscopic density defined by $ρ(t,x) = \int_{\Rd} f(t,x,ξ)dξ$ is bounded in $\Linf$. Our proof is based on optimal transportation.