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Landau damping in Sobolev spaces for the Vlasov-HMF model (1403.1668v2)
Published 7 Mar 2014 in math.AP
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.
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