Uniformly Rotating Vortex Patches with 90-Degree Corners

[2608.13134] Uniformly Rotating Vortex Patches with 90-Degree Corners Skip to main content Search Submit Donate Log in Mathematics > Analysis of PDEs arXiv:2608.13134 (math) [Submitted on 13 Aug 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Uniformly Rotating Vortex Patches with 90-Degree Corners Authors: De Huang , Jiajun Tong , Xiaopeng Zheng View PDF HTML (experimental) Abstract: For the 2-D incompressible Euler equation, we prove the existence of $m$-fold symmetric uniformly rotating vortex patches with 90-degree corners for all $m\geq 12$. Properties of these patches and the induced stationary flows in the co-rotating frame are characterized. Our construction is based on a novel fixed-point method. Comments: 115 pages, 6 figures. Minor changes in language compared with v1. An expanded table of contents is also provided for readers' convenience Subjects: Analysis of PDEs (math.AP) ; Fluid Dynamics (physics.flu-dyn) MSC classes: Primary: 35Q31, 76B03, 76B47, Secondary: 35R35 Cite as: arXiv:2608.13134 [math.AP] (or arXiv:2608.13134v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2608.13134 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jiajun Tong [ view email ] [v1] Thu, 13 Aug 2026 12:09:03 UTC (4,391 KB) [v2] Thu, 27 Aug 2026 08:49:54 UTC (4,391 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2026-08 Change to browse by: math physics physics.flu-dyn References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation 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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