Inverse modified scattering and polyhomogeneous expansions for the Vlasov--Poisson system
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913328065937408 |
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| author | Schlue, Volker Taylor, Martin |
| author_facet | Schlue, Volker Taylor, Martin |
| contents | We give a new proof of well posedness of the inverse modified scattering problem for the Vlasov--Poisson system: for every suitable scattering profile there exists a solution of Vlasov--Poisson which disperses and scatters, in a modified sense, to this profile. Further, as a consequence of the proof, the solutions are shown to admit a polyhomogeneous expansion, to any finite but arbitrarily high order, with coefficients given explicitly in terms of the scattering profile. The proof does not exploit the full ellipticity of the Poisson equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_15885 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse modified scattering and polyhomogeneous expansions for the Vlasov--Poisson system Schlue, Volker Taylor, Martin Analysis of PDEs Mathematical Physics We give a new proof of well posedness of the inverse modified scattering problem for the Vlasov--Poisson system: for every suitable scattering profile there exists a solution of Vlasov--Poisson which disperses and scatters, in a modified sense, to this profile. Further, as a consequence of the proof, the solutions are shown to admit a polyhomogeneous expansion, to any finite but arbitrarily high order, with coefficients given explicitly in terms of the scattering profile. The proof does not exploit the full ellipticity of the Poisson equation. |
| title | Inverse modified scattering and polyhomogeneous expansions for the Vlasov--Poisson system |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2404.15885 |