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
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 LMO - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

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