On Linear Damping Around Inhomogeneous Stationary States of the Vlasov-HMF Model
arXiv:2105.02484
Abstract
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.
References in corpus (11)
- On Landau damping
- Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
- Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model
- Lynden-Bell and Tsallis distributions for the HMF model
- The Vlasov equation and the Hamiltonian Mean-Field model
- Algebraic damping in the one-dimensional Vlasov equation
- Landau damping in Sobolev spaces for the Vlasov-HMF model
- Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model
- Inhomogeneous Tsallis distributions in the HMF model
- On the linearized Vlasov-Poisson system on the whole space around stable homogeneous equilibria
- Exponential dephasing of oscillators in the Kinetic Kuramoto Model