Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data

Laurent Lafleche

doi:10.1016/j.anihpc.2021.01.004

JournalsaihpcVol. 38, No. 6pp. 1739–1762

Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data

Laurent Lafleche
CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, PSL Research University, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France; CMLS, École polytechnique, CNRS, Université Paris-Saclay, 91128 Palaiseau cedex, France

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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 $d \geq 3$ , 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 bounds on the space and velocity moments of even order and the asymptotic behavior of the spatial density due to dispersion effects, uniform in the Planck constant $ħ$ .

Cite this article

Laurent Lafleche, Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 6, pp. 1739–1762

DOI 10.1016/J.ANIHPC.2021.01.004