On algebraic damping close to inhomogeneous Vlasov equilibria in multi-dimensional spaces

Abstract

We investigate the asymptotic damping of a perturbation around inhomogeneous stable stationary states of the Vlasov equation in spatially multi-dimensional systems. We show that branch singularities of the Fourier-Laplace transform of the perturbation yield algebraic dampings. In two spatial dimensions, we classify the singularities and compute the associated damping rate and frequency. This 2D setting also applies to spherically symmetric self-gravitating systems. We validate the theory using a toy model and an advection equation associated with the isochrone model, a model of spherical self-gravitating systems.

37 pages, 10 figures

References in corpus (5)

• Small BGK waves and nonlinear Landau damping
• Algebraic damping in the one-dimensional Vlasov equation
• Relaxation times of unstable states in systems with long range interactions
• Dynamical stability criterion for inhomogeneous quasi-stationary states in long-range systems
• Stability of inhomogeneous states in mean-field models with a local potential

Cited by in corpus (3)

• Symplectic coarse graining approach to the dynamics of spherical self-gravitating systems
• The asymptotic behavior of the Reidemeister torsion for Seifert manifolds and PSL(2;R)-representations of Fuchsian groups
• Damping versus oscillations for a gravitational Vlasov-Poisson system