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

Grégoire Loeper

doi:10.1016/j.matpur.2006.01.005

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

Grégoire Loeper

Research output: Contribution to journal › Article › Research › peer-review

125 Citations (Scopus)

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) = ∫_R^d f (t, x, ξ) d ξ is bounded in L^∞. Our proof is based on optimal transportation.

Original language	English
Pages (from-to)	68-79
Number of pages	12
Journal	Journal des Mathematiques Pures et Appliquees
Volume	86
Issue number	1
DOIs	https://doi.org/10.1016/j.matpur.2006.01.005
Publication status	Published - Jul 2006
Externally published	Yes

Keywords

Optimal transportation
Transport equations
Vlasov-Poisson system

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10.1016/j.matpur.2006.01.005

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.",

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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.

KW - Optimal transportation

KW - Transport equations

KW - Vlasov-Poisson system

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

Abstract

Keywords

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