Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations

[2412.04581] Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2412.04581 (math) [Submitted on 5 Dec 2024 ( v1 ), last revised 10 Apr 2026 (this version, v3)] Title: Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations Authors: Nuno J. Alves , Peter Markowich , Athanasios E. Tzavaras View a PDF of the paper titled Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations, by Nuno J. Alves and 2 other authors View PDF HTML (experimental) Abstract: We study a one-dimensional nonlinear Vlasov equation with a local self-consistent force field generated by the density, where the force is given by the spatial derivative of a real-analytic nonlinearity. For small analytic initial data, we prove local-in-time existence and uniqueness of analytic solutions. In particular, this yields a perturbative well-posedness result around the trivial equilibrium. We also give an energy-based representation of weak stationary states and discuss perturbations around spatially homogeneous stationary profiles. The proof relies on a contraction mapping argument in a complete metric space of analytic functions. As a technical byproduct, we establish quantitative composition estimates for analytic nonlinearities in the analytic norms used in the argument. Subjects: Analysis of PDEs (math.AP) MSC classes: Primary: 35Q83, Secondary: 35F25, 82D10 Cite as: arXiv:2412.04581 [math.AP] (or arXiv:2412.04581v3 [math.AP] for this version) https://doi.org/10.48550/arXiv.2412.04581 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nuno J. Alves [ view email ] [v1] Thu, 5 Dec 2024 19:55:30 UTC (19 KB) [v2] Mon, 2 Mar 2026 17:09:28 UTC (29 KB) [v3] Fri, 10 Apr 2026 06:57:02 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Local analytic well-posedness for one-dimensional Vlasov$\unicode{x2013}$Dirac$\unicode{x2013}$Benney-type equations, by Nuno J. Alves and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2024-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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