Nonlinear Landau damping and wave operators in sharp Gevrey spaces
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929337192677376 |
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| author | Ionescu, A. D. Pausader, B. Wang, X. Widmayer, K. |
| author_facet | Ionescu, A. D. Pausader, B. Wang, X. Widmayer, K. |
| contents | We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria.
We also prove the existence of nonlinear scattering operators associated to the confined Vlasov-Poisson evolution, as well as suitable injectivity properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these operators.
Our results give definitive answers to two well-known open problems in the field, both of them stated in the recent review of Bedrossian [4, Section 6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Landau damping and wave operators in sharp Gevrey spaces Ionescu, A. D. Pausader, B. Wang, X. Widmayer, K. Analysis of PDEs Mathematical Physics We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the existence of nonlinear scattering operators associated to the confined Vlasov-Poisson evolution, as well as suitable injectivity properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these operators. Our results give definitive answers to two well-known open problems in the field, both of them stated in the recent review of Bedrossian [4, Section 6]. |
| title | Nonlinear Landau damping and wave operators in sharp Gevrey spaces |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2405.04473 |