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Article Dans Une Revue Contemporary mathematics Année : 2018

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

Evelyne Miot
Thomas Holding
  • Fonction : Auteur

Résumé

In this paper, we establish uniqueness of the solution of the Vlasov-Poisson system with spatial density belonging to a certain class of Orlicz spaces. This extends the uniqueness result of Loeper [11] (which holds for density in L-infinity) and of the paper [15]. Uniqueness is a direct consequence of our main result, which provides a quantitative stability estimate for the Wasserstein distance between two weak solutions with spatial density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability for mean-field PDEs. Our proofs are built on the second-order structure of the underlying characteristic system associated to the equation.

Dates et versions

hal-01760786 , version 1 (06-04-2018)

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Citer

Evelyne Miot, Thomas Holding. Uniqueness and stability for the Vlasov-Poisson system with spatial density in Orlicz spaces. Contemporary mathematics, 2018, Mathematical Analysis in Fluid Mechanics: Selected Recent Results, 710, pp.145-162. ⟨10.1090/conm/710/14368⟩. ⟨hal-01760786⟩
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