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In this paper, we establish uniqueness of the solution of the Vlasov-Poissonsystem with spatial density belonging to a certain class of Orlicz spaces. Thisextends the uniqueness result of Loeper (which holds for uniformly boundeddensity) and the uniqueness result of the second author. Uniqueness is a directconsequence of our main result, which provides a quantitative stabilityestimate for the Wasserstein distance between two weak solutions with spatialdensity in such Orlicz spaces, in the spirit of Dobrushin's proof of stabilityfor mean-field PDEs. Our proofs are built on the second-order structure of theunderlying characteristic system associated to the equation.

Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces