We study the dynamics of perturbations around an inhomogeneous stationary state of the Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion (Penrose criterion). We consider solutions of the linearized equation around the steady state, and prove the algebraic decay in time of the Fourier modes of their density. We prove moreover that these solutions exhibit a scattering behavior to a modified state, implying a linear Landau damping effect with an algebraic rate of damping.

中文翻译：

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Vlasov-HMF模型非均匀平稳态周围的线性阻尼

我们研究了满足线性稳定准则（Penrose准则）的Vlasov-HMF（哈密尔顿平均场）模型的非均匀平稳状态周围的摄动动力学。我们考虑稳态下线性化方程的解，并证明其密度的傅立叶模态随时间的代数衰减。此外，我们证明了这些解表现出了修正状态的散射行为，这意味着具有代数阻尼率的线性Landau阻尼效应。