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The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature
- Publication Year :
- 2015
-
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.<br />Comment: 34 pages, 2 figures
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1506.07090
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00220-016-2608-9