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

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Abstract

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
Volume86
Issue number1
DOIs
Publication statusPublished - Jul 2006
Externally publishedYes

Keywords

  • Optimal transportation
  • Transport equations
  • Vlasov-Poisson system

Cite this

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abstract = "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.",
keywords = "Optimal transportation, Transport equations, Vlasov-Poisson system",
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Uniqueness of the solution to the Vlasov-Poisson system with bounded density. / Loeper, Grégoire.

In: Journal des Mathematiques Pures et Appliquees, Vol. 86, No. 1, 07.2006, p. 68-79.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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.

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