Long-time dynamics of Vlasov--Hartree systems across the Coulomb threshold

[2608.04402] Long-time dynamics of Vlasov--Hartree systems across the Coulomb threshold Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2608.04402 (math) [Submitted on 5 Aug 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Long-time dynamics of Vlasov--Hartree systems across the Coulomb threshold Authors: Wenrui Huang , Mengyi Xie View a PDF of the paper titled Long-time dynamics of Vlasov--Hartree systems across the Coulomb threshold, by Wenrui Huang and Mengyi Xie View PDF HTML (experimental) Abstract: We study the three-dimensional Vlasov--Hartree system with Coulomb and inverse-power interactions. For small, regular, localized data, we prove global well-posedness and determine long-time dynamics. The main result concerns the Coulomb case, where the coupling persists at leading order through reciprocal asymptotic corrections: the fermionic distribution scatters along logarithmically corrected free characteristics set by the asymptotic bosonic profile, while the bosonic wave gains a logarithmic phase set by the asymptotic fermionic density. We also treat longer- and shorter-range interactions. Our proof combines Hamiltonian methods for the Vlasov equation with purely physical-space vector-field methods for dispersive equations. For stronger long-range interactions, we introduce a symplectic transformation and a regularized effective-phase cancellation, which remove leading nonintegrable interactions while preserving Hamiltonian structure and avoiding derivative loss. Comments: minor revision and added the longer-range interactions Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2608.04402 [math.AP] (or arXiv:2608.04402v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2608.04402 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mengyi Xie [ view email ] [v1] Wed, 5 Aug 2026 03:14:08 UTC (27 KB) [v2] Fri, 14 Aug 2026 22:52:12 UTC (46 KB) Full-text links: Access Paper: View a PDF of the paper titled Long-time dynamics of Vlasov--Hartree systems across the Coulomb threshold, by Wenrui Huang and Mengyi Xie View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-08 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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