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

Grégoire Loeper

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125 Citations (Scopus)


In this paper, 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) = ∫Rd f (t, x, ξ) d ξ is bounded in L. Our proof is based on optimal transportation.

Original languageEnglish
Pages (from-to)68-79
Number of pages12
JournalJournal des Mathematiques Pures et Appliquees
Issue number1
Publication statusPublished - Jul 2006
Externally publishedYes


  • Optimal transportation
  • Transport equations
  • Vlasov-Poisson system

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