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Landau Damping in Sobolev Spaces for the Vlasov-HMF Model

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Abstract

We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.

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Authors and Affiliations

  1. INRIA& ENS Cachan Bretagne, Avenue Robert Schumann, 35170, Bruz, France

    Erwan Faou

  2. Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud et Institut Universitaire de France, Orsay, France

    Frédéric Rousset

Authors
  1. Erwan Faou
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  2. Frédéric Rousset
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Correspondence to Frédéric Rousset.

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Communicated by C. Dafermos

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Faou, E., Rousset, F. Landau Damping in Sobolev Spaces for the Vlasov-HMF Model. Arch Rational Mech Anal 219, 887–902 (2016). https://doi.org/10.1007/s00205-015-0911-9

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  • DOI: https://doi.org/10.1007/s00205-015-0911-9

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