Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data

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dc.creatorHwang, Hyung Ju
dc.creatorRendall, Alan D.
dc.creatorVelazquez, Juan J. L.
dc.date2006-06-16
dc.date.accessioned2026-07-07T07:17:21Z
dc.date.available2026-07-07T07:17:21Z
dc.descriptionThe Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so that in $N$ dimensions for $N\ge 3$ the derivative of the density of order $k$ decays like $t^{-N-k}$. An asymptotic formula for the solution at late times is also obtained.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/math/0606389
dc.identifierhttp://arxiv.org/abs/math/0606389
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113908
dc.subjectAnalysis of PDEs
dc.subject35B40
dc.titleOptimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data
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