[2310.09752] Existence of steady Navier-Stokes flows exterior to an infinite cylinder Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2310.09752 (math) [Submitted on 15 Oct 2023 ( v1 ), last revised 25 Apr 2026 (this version, v3)] Title: Existence of steady Navier-Stokes flows exterior to an infinite cylinder Authors: Mitsuo Higaki , Ryoma Horiuchi View a PDF of the paper titled Existence of steady Navier-Stokes flows exterior to an infinite cylinder, by Mitsuo Higaki and 1 other authors View PDF HTML (experimental) Abstract: We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal infinity. More precisely, for a boundary datum determined by a rotating flow and a suction flow, and for a small force of the form $f=g+\operatorname{div} F$ with suitable decay, we prove the existence of a weak solution asymptotic to the corresponding Hamel-type flow. Although all data are independent of the vertical variable, the problem is not reduced to the planar exterior Navier-Stokes system: the vertical component satisfies a separate transport-diffusion equation involving the two-dimensional Laplacian, whose fundamental solution has logarithmic growth. The proof is based on a mode-by-mode analysis of the linearized three-dimensional problem around the Hamel-type flow and a contraction argument. Comments: 18 pages. Abstract rewritten, introduction expanded, and references added. No changes to the main mathematical results Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2310.09752 [math.AP] (or arXiv:2310.09752v3 [math.AP] for this version) https://doi.org/10.48550/arXiv.2310.09752 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mitsuo Higaki [ view email ] [v1] Sun, 15 Oct 2023 06:34:55 UTC (18 KB) [v2] Wed, 8 Nov 2023 22:21:28 UTC (18 KB) [v3] Sat, 25 Apr 2026 04:03:05 UTC (17 KB) Full-text links: Access Paper: View a PDF of the paper titled Existence of steady Navier-Stokes flows exterior to an infinite cylinder, by Mitsuo Higaki and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2023-10 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