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arXiv · 1506.07090

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

Florin Diacu·Slim Ibrahim·Crystal Lind·Shengyi Shen
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Abstract

We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $κ\ne 0$: the unit sphere $\mathbb S^2$, for $κ>0$, and the unit hyperbolic sphere $\mathbb H^2$, for $κ<0$. 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.

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Florin Diacu, Slim Ibrahim, Crystal Lind, Shengyi Shen. 2015-06-23. The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature. https://doi.org/10.1007/s00220-016-2608-9

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