A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity

[2608.15174] A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2608.15174 (math) [Submitted on 15 Aug 2026] Title: A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity Authors: Jiajie Chen , Thomas Y. Hou View a PDF of the paper titled A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity, by Jiajie Chen and Thomas Y. Hou View PDF HTML (experimental) Abstract: In \cite{zhang2025dimension}, the author discusses the applicability of a nonexistence result for self-similar profiles to the Hou--Luo scenario and raises questions about the approximate self-similar profile constructed in \cite{ChenHou2023a,ChenHou2023b}. In this note, we clarify two main points. First, the far-field discrepancy identified in \cite{zhang2025dimension} is the raw nonlocal Poisson error, not the profile residual error used in the stability proof of \cite{ChenHou2023a,ChenHou2023b}. The relevant nonlocal contribution to the profile residual contains the nonlocal velocity error multiplied by additional decaying factors, which provide crucial smallness in the far field estimates. Second, we examine the figure-based evidence used in \cite[Remark 2.4]{zhang2025dimension} to support the applicability of the assumption in \cite[Proposition 2.3(i)]{zhang2025dimension}, and show that the same grid-point data do not support that interpretation. Thus the comparisons and figure-based evidence in \cite{zhang2025dimension} neither invalidate the residual estimates in \cite{ChenHou2023a,ChenHou2023b} nor justify the claimed applicability of the angular-increase assumption to the Hou--Luo scenario. Comments: 7 pages Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2608.15174 [math.AP] (or arXiv:2608.15174v1 [math.AP] for this version) https://doi.org/10.48550/arXiv.2608.15174 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jiajie Chen [ view email ] [v1] Sat, 15 Aug 2026 11:26:16 UTC (2,448 KB) Full-text links: Access Paper: View a PDF of the paper titled A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity, by Jiajie Chen and Thomas Y. Hou 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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