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Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system

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Summary

We prove that, if the initial data has moments inv higher than three, then the solution of Vlasov-Poisson has also moments inv higher than three. We deduce from this different regularity results on the local density, the force field or the solution itself. Also we give a new uniqueness result, and new regularity results for solutions satisfying only the energy andL ∞ bounds. Our proofs are based on a new representation formula and logarithmic estimates for the force field.

Résumé

Nous montrons que, si la donnée initiale possède des moments env plus élevés que trois, alors la solution de l'Equation de Vlasov-Poisson a aussi des moments plus élevés que trois. Nous en déduisons différents résultats de régularité sur la densité locale, le champ de force ou la solution elle-même. Nous donnons également un nouveau résultat d'unicité et de nouveaux résultats de régularité pour les solutions vérifiant uniquement les estimations d'énergie et les bornesL ∞. Nos démonstrations sont fondés sur une nouvelle formule de représentation et des estimées logarithmiques sur le champ de force.

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Authors and Affiliations

  1. CEREMADE, Université Paris IX-Dauphine, Place de Lattre de Tassigny, F-75775, Paris Cedex 16

    P. L. Lions

  2. Département de Mathématiques, Université d'Orléans, BP 6759, F-45067, Orléans Cedex 2

    B. Perthame

Authors
  1. P. L. Lions
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  2. B. Perthame
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Oblatum 14-I-1991

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Lions, P.L., Perthame, B. Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system. Invent Math 105, 415–430 (1991). https://doi.org/10.1007/BF01232273

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