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arXiv · 2412.01544

Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm

Håkan Andréasson·Markus Kunze·Gerhard Rein
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Abstract

We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov-Poisson system and to the Einstein-Vlasov system. There are several reasons why a mathematical analysis of this numerical scheme is important. A generalization of the present result to the case of flat axially symmetric solutions would prove that the steady states obtained numerically in \cite{AR3} do exist. Moreover, in the relativistic case the question whether a steady state can be obtained by this scheme seems to be related to its dynamical stability. This motivates the desire for a deeper understanding of this strategy.

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Håkan Andréasson, Markus Kunze, Gerhard Rein. 2024-12-02. Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm. https://arxiv.org/abs/2412.01544

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