Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910367399018496 |
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| author | Iacobelli, Mikaela Junné, Jonathan |
| author_facet | Iacobelli, Mikaela Junné, Jonathan |
| contents | We extend Loeper's $L^2$-estimate relating the electric fields to the densities for the Vlasov-Poisson system to $L^p$, with $1 < p < +\infty$, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical Loeper's $2$-Wasserstein stability estimate and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance to kinetic Wasserstein distances of order $1 < p < +\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09293 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances Iacobelli, Mikaela Junné, Jonathan Analysis of PDEs Mathematical Physics 35Q83, 82C40, 82D10, 35B35 We extend Loeper's $L^2$-estimate relating the electric fields to the densities for the Vlasov-Poisson system to $L^p$, with $1 < p < +\infty$, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical Loeper's $2$-Wasserstein stability estimate and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance to kinetic Wasserstein distances of order $1 < p < +\infty$. |
| title | Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances |
| topic | Analysis of PDEs Mathematical Physics 35Q83, 82C40, 82D10, 35B35 |
| url | https://arxiv.org/abs/2212.09293 |