Orateur
Erwan Faou
(INRIA)
Description
We study the dynamics of perturbations around inhomogeneous stationary states of the Vlasov-HMF (Hamiltonian Mean-Field) model. These stationary solutions are built with compact support and satisfy a linearized stability criterion (Penrose criterion). We show a scattering behavior to a modified state over long (but finite) time depending on the size of the perturbation. This implies a damping effect with an algebraic rate. The key ingredients are based on the analysis of echoes in the dynamics generated by the action-angle variables of the inhomogenous stationary state. This is a joint work with Torryanand Seetohul and Frédéric Rousset.