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Global Semiclassical Limit from Hartree to Vlasov Equation for Concentrated Initial Data

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Vlasov2.pdf (360.5Kb)
Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
02-2019
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-02046481
Dewey
Analyse
Sujet
Hartree equation; Nonlinear Schrödinger equation; Vlasov equation; Coulomb interaction; gravitational interaction; semiclassical limit
URI
https://basepub.dauphine.fr/handle/123456789/18578
Collections
  • CEREMADE : Publications
Metadata
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Author
Lafleche, Laurent
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
20
Abstract (EN)
We prove a quantitative and global in time semiclassical limit from the Hartree to the Vlasov equation in the case of a singular interaction potential in dimension d ≥ 3, including the case of a Coulomb singularity in dimension d = 3. This result holds for initial data concentrated enough in the sense that some space moments are initially sufficiently small. As an intermediate result, we also obtain quantitative semiclassical bounds on the space and velocity moments of even order and the asymptotic behaviour of the spatial density due to dispersion effects.

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