On quantitative linear gravitational relaxation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908372842840064 |
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| author | Hadzic, Mahir Schrecker, Matthew |
| author_facet | Hadzic, Mahir Schrecker, Matthew |
| contents | We prove quantitative decay rates for the linearised Vlasov-Poisson system around compactly supported equilibria. More precisely, we prove decay of the gravitational potential induced by the radial dynamics of this system in the presence of a point mass source. Our result can be interpreted as the gravitational version of linear Landau damping in the radial setting and hence the first linear asymptotic stability result around such equilibria. We face fundamental obstacles to decay caused by the presence of stable trapping in the problem. To overcome these issues we introduce several new ideas. We use different tools, including the Birkhoff-Poincaré normal form, action-angle type variables, and delicate resolvent bounds to prove a suitable version of the limiting absorption principle and obtain the decay-in-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On quantitative linear gravitational relaxation Hadzic, Mahir Schrecker, Matthew Analysis of PDEs Mathematical Physics 35Q83, 35Q85, 35P25, 35B40, 35Q75 We prove quantitative decay rates for the linearised Vlasov-Poisson system around compactly supported equilibria. More precisely, we prove decay of the gravitational potential induced by the radial dynamics of this system in the presence of a point mass source. Our result can be interpreted as the gravitational version of linear Landau damping in the radial setting and hence the first linear asymptotic stability result around such equilibria. We face fundamental obstacles to decay caused by the presence of stable trapping in the problem. To overcome these issues we introduce several new ideas. We use different tools, including the Birkhoff-Poincaré normal form, action-angle type variables, and delicate resolvent bounds to prove a suitable version of the limiting absorption principle and obtain the decay-in-time. |
| title | On quantitative linear gravitational relaxation |
| topic | Analysis of PDEs Mathematical Physics 35Q83, 35Q85, 35P25, 35B40, 35Q75 |
| url | https://arxiv.org/abs/2505.14856 |