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MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION

Abstract : This paper proves the validity of the joint mean-field and classical limit of the quantum N-body dynamics leading to the pressureless Euler-Poisson system for factorized initial data whose first marginal has a monokinetic Wigner measure. The interaction potential is assumed to be the repulsive Coulomb potential. The validity of this derivation is limited to finite time intervals on which the Euler-Poisson system has a smooth solution that is rapidly decaying at infinity. One key ingredient in the proof is an inequality from [S. Serfaty, with an appendix of M. Duerinckx arXiv:1803.08345v3 [math.AP]].
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Submitted on : Monday, December 9, 2019 - 9:11:03 PM
Last modification on : Tuesday, May 17, 2022 - 11:45:10 AM
Long-term archiving on: : Tuesday, March 10, 2020 - 9:48:15 PM

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François Golse, Thierry Paul. MEAN-FIELD AND CLASSICAL LIMIT FOR THE N-BODY QUANTUM DYNAMICS WITH COULOMB INTERACTION. Communications on Pure and Applied Mathematics, Wiley, 2022, ⟨10.1002/cpa.21986⟩. ⟨hal-02361050v2⟩

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