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On Linear Damping around Inhomogeneous Stationary States of the Vlasov-HMF Model

Erwan Faou 1 Romain Horsin 2 Frédéric Rousset 3
1 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We study the dynamics of perturbations around an inhomogeneous stationary state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion (Penrose criterion). We consider solutions of the linearized equation around the steady state, and prove the algebraic decay in time of the Fourier modes of their density. We prove moreover that these solutions exhibit a scattering behavior to a modified state, implying a linear Landau damping effect with an algebraic rate of damping.
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Submitted on : Wednesday, May 5, 2021 - 12:56:18 PM
Last modification on : Friday, May 20, 2022 - 9:04:53 AM
Long-term archiving on: : Friday, August 6, 2021 - 6:38:25 PM

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Erwan Faou, Romain Horsin, Frédéric Rousset. On Linear Damping around Inhomogeneous Stationary States of the Vlasov-HMF Model. Journal of Dynamics and Differential Equations, Springer Verlag, 2021, 33 - special issue (3), pp.1531-1577. ⟨10.1007/s10884-021-10044-y⟩. ⟨hal-03218110⟩

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