English

Landau damping in Sobolev spaces for the Vlasov-HMF model

Analysis of PDEs 2016-01-27 v2

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.

Keywords

Cite

@article{arxiv.1403.1668,
  title  = {Landau damping in Sobolev spaces for the Vlasov-HMF model},
  author = {Erwan Faou and Frédéric Rousset},
  journal= {arXiv preprint arXiv:1403.1668},
  year   = {2016}
}