%0 Journal Article
%T The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature
%A Florin Diacu
%A Slim Ibrahim
%A Crystal Lind
%A Shengyi Shen
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1506.07090v1