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Inverse modified scattering and polyhomogeneous expansions for the Vlasov--Poisson system

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arxiv 2404.15885 v1 pith:2FDXF6X2 submitted 2024-04-24 math.AP math-phmath.MP

Volker Schlue , Martin Taylor This is my paper · ORCID
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keywords scatteringmodifiedprofileproofvlasov--poissoninversepolyhomogeneoussystem
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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.

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Cited by 1 Pith paper

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  1. Arbitrary Polynomial Decay Rates of Neutral, Collisionless Plasmas

    math.AP 2025-02 conditional novelty 8.0 of 10

    Neutral Vlasov-Poisson plasmas can be constructed to exhibit arbitrarily fast polynomial decay of charge density and electric field, at rates t^{-m-3} and t^{-m-2} for any integer m.

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