Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions

[2608.04104] Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2608.04104 (math) [Submitted on 4 Aug 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions Authors: Mitia Duerinckx , Pierre-Emmanuel Jabin View a PDF of the paper titled Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions, by Mitia Duerinckx and 1 other authors View PDF HTML (experimental) Abstract: We obtain the first derivation of the 2D Vlasov-Poisson equation for classical particles with Coulomb interactions without any microscopic cutoff. The proof relies on our recent dual hierarchical approach to mean-field limits, together with a refined analysis of dual BBGKY hierarchies on linearized correlations, based on kinetic regularization effects. The result holds more generally for arbitrary singular interaction forces $K\in L^{2-\eta}_{loc}$ with $\eta>0$ small enough, in any dimension, and it extends to Brownian particles. It holds globally in time as long as the mean-field solution is regular enough. Comments: 36 pages Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph) Cite as: arXiv:2608.04104 [math.AP] (or arXiv:2608.04104v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2608.04104 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mitia Duerinckx [ view email ] [v1] Tue, 4 Aug 2026 18:01:09 UTC (29 KB) [v2] Sat, 15 Aug 2026 10:58:14 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions, by Mitia Duerinckx and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-08 Change to browse by: math math-ph math.MP 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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