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From the Hartree to the Vlasov Dynamics: Conditional Strong Convergence

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From Particle Systems to Partial Differential Equations (ICPS 2019, ICPS 2018, ICPS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 352))

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Abstract

We review the recent results [45, 46] concerning the semiclassical limit from the Hartree dynamics to the Vlasov equation with singular potentials and extend them to the case of more general radial interactions. We prove that, at positive temperature, the Hartree dynamics converges in trace norm to the Vlasov one, for a particular class of initial states.

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Notes

  1. 1.

    Such a solution indeed exists if the initial data are sufficiently regular. For the precise assumptions, see Remark 3 below.

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Acknowledgements

The author acknowledges the support of the Swiss National Science Foundation through the Eccellenza project PCEFP2_181153 and of the NCCR SwissMAP.

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Authors and Affiliations

  1. Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051, Basel, Switzerland

    Chiara Saffirio

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  1. Chiara Saffirio
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Correspondence to Chiara Saffirio .

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Editors and Affiliations

  1. Laboratoire J.A. Dieudonné, UMR CNRS-UNS, Université Côte d’Azur, Nice Cedex 02, France

    Cédric Bernardin

  2. Centre de Math. Laurent Schwartz (CMLS), École Polytechnique, CMLS, Palaiseau Cedex, France

    François Golse

  3. Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal

    Patrícia Gonçalves

  4. Dipartimento di Matematica e Informatica, Università di Palermo, Palermo, Italy

    Valeria Ricci

  5. Centro de Matemática, Universidade do Minho, Braga, Portugal

    Ana Jacinta Soares

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Saffirio, C. (2021). From the Hartree to the Vlasov Dynamics: Conditional Strong Convergence. In: Bernardin, C., Golse, F., Gonçalves, P., Ricci, V., Soares, A.J. (eds) From Particle Systems to Partial Differential Equations. ICPS ICPS ICPS 2019 2018 2017. Springer Proceedings in Mathematics & Statistics, vol 352. Springer, Cham. https://doi.org/10.1007/978-3-030-69784-6_16

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