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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02046481
Contributor : Laurent Lafleche Connect in order to contact the contributor
Submitted on : Tuesday, December 14, 2021 - 12:02:28 PM
Last modification on : Sunday, June 26, 2022 - 3:25:02 AM

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  • HAL Id : hal-02046481, version 2

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Laurent Lafleche. Global Semiclassical Limit from Hartree to Vlasov Equation for Concentrated Initial Data. 2019. ⟨hal-02046481v2⟩

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