Landau Damping in Sobolev Spaces for the Vlasov-HMF Model |
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| Authors: | Erwan Faou Frédéric Rousset |
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| Institution: | 1. INRIA& ENS Cachan Bretagne, Avenue Robert Schumann, 35170, Bruz, France
2. Laboratoire de Mathématiques d’Orsay (UMR 8628), Université Paris-Sud et Institut Universitaire de France, Orsay, France
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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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