Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918108949643264 |
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| author | Andréasson, Håkan Kunze, Markus Rein, Gerhard |
| author_facet | Andréasson, Håkan Kunze, Markus Rein, Gerhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01544 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm Andréasson, Håkan Kunze, Markus Rein, Gerhard Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics 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. |
| title | Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2412.01544 |