The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature

Abstract

We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $\kappa \ne 0$: the unit sphere ${\mathbb{S}}^2$, for $\kappa >0$, and the unit hyperbolic sphere ${\mathbb{H}}^2$, for $\kappa <0$. These equations can be easily generalized to higher dimensions. When the particles move on a geodesic, the system reduces to a 1-dimensional problem that is more singular than the classical analogue of the Vlasov-Poisson system. In the analysis of this reduced model, we study the well-posedness of the problem and derive Penrose-type conditions for linear stability around homogeneous solutions in the sense of Landau damping.

34 pages, 2 figures

References in corpus (1)

• Landau damping in Sobolev spaces for the Vlasov-HMF model

Cited by in corpus (3)

• On propagation of higher space regularity for non-linear Vlasov equations
• The continuous transition of Hamiltonian vector fields through manifolds of constant curvature
• Semiclassical limit of orthonormal Strichartz estimates on scattering manifolds