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• W2802411584 endingPage "2150029" @default.
• W2802411584 startingPage "2150029" @default.
• W2802411584 abstract "In this work, we show convergence of the [Formula: see text]-particle bosonic Schrödinger equation towards the Hartree equation. Hereby, we extend the results of [I. Anapolitanos and M. Hott, A simple proof of convergence to the Hartree dynamics in Sobolev trace norms, J. Math. Phys. 57(12) (2016) 122108; I. Anapolitanos, M. Hott and D. Hundertmark, Derivation of the Hartree equation for compound Bose gases in the mean field limit, Rev. Math. Phys. 29(07) (2017) 1750022]. We first consider the semi-relativistic Hartree equation in the defocusing and the focusing cases. We show that Pickl’s projection method [P. Pickl, Derivation of the time dependent Gross–Pitaevskii equation without positivity condition on the interaction, J. Statist. Phys. 140(1) (2010) 76–89; P. Pickl, A simple derivation of mean field limits for quantum systems, Lett. Math. Phys. 97(2) (2011) 151–164; P. Pickl, Derivation of the time dependent Gross–Pitaevskii equation with external fields, Rev. Math. Phys. 27(1) (2015) 1550003], can be adapted to this problem. Next, we extend this result to the case of fractional Hartree equations with potentials that are more singular than the Coulomb potential. Finally, in the non-relativistic case, we derive the Hartree equation assuming only [Formula: see text] initial data for potentials with a quantitative bound on the convergence rate." @default.
• W2802411584 created "2018-05-17" @default.
• W2802411584 creator A5027100283 @default.
• W2802411584 date "2021-06-04" @default.
• W2802411584 modified "2023-09-23" @default.
• W2802411584 title "Convergence rate towards the fractional Hartree equation with singular potentials in higher Sobolev trace norms" @default.
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• W2802411584 doi "https://doi.org/10.1142/s0129055x2150029x" @default.
• W2802411584 hasPublicationYear "2021" @default.
• W2802411584 type Work @default.

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