arXiv:1403.1668 Abstract | arXiv Analytics

arXiv:1403.1668 [math.AP]Abstract References Reviews Resources

Landau damping in Sobolev spaces for the Vlasov-HMF model

Published 2014-03-07, updated 2014-04-18Version 2

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.

DOI: 10.1007/s00205-015-0911-9

Categories: math.AP

Keywords: sobolev spaces, vlasov-hmf model, small sobolev neighborhood, nonlinear landau damping effect, linearized stability criterion

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