Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant
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| Format: | Preprint |
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2014
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| _version_ | 1866916288924745728 |
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| author | Nungesser, Ernesto |
| author_facet | Nungesser, Ernesto |
| contents | We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringström shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1402_7085 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant Nungesser, Ernesto Mathematical Physics General Relativity and Quantum Cosmology We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringström shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion. |
| title | Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant |
| topic | Mathematical Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/1402.7085 |