On the stability of vacuum in the screened Vlasov-Poisson equation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912937734569984 |
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| author | Iacobelli, Mikaela Rossi, Stefano Widmayer, Klaus |
| author_facet | Iacobelli, Mikaela Rossi, Stefano Widmayer, Klaus |
| contents | We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on $\mathbb{R}^d\times\mathbb{R}^d$ near vacuum. We show that for dimensions $d\geq 2$, under mild assumptions on localization (in terms of spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions scatter freely. In dimension $d=1$, we obtain a long time existence result in analytic regularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_17978 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stability of vacuum in the screened Vlasov-Poisson equation Iacobelli, Mikaela Rossi, Stefano Widmayer, Klaus Analysis of PDEs Mathematical Physics 35B40, 35B35, 35F20 We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on $\mathbb{R}^d\times\mathbb{R}^d$ near vacuum. We show that for dimensions $d\geq 2$, under mild assumptions on localization (in terms of spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions scatter freely. In dimension $d=1$, we obtain a long time existence result in analytic regularity. |
| title | On the stability of vacuum in the screened Vlasov-Poisson equation |
| topic | Analysis of PDEs Mathematical Physics 35B40, 35B35, 35F20 |
| url | https://arxiv.org/abs/2410.17978 |