Landau damping in Sobolev spaces for the Vlasov-HMF model
  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. 
Erwan Faou (INRIA - IRMAR, IRMAR), Fr\'ed\'eric Rousset (LM-Orsay)
math.AP