{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0adc635518dbf572fb97475970a6962c57599a70640fb8e8528ffa4758012a05","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"6ea08c5abeb9a9d0a3009bca1c3510932071136545af2148935f8231a9c5cc22","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.fluid-singularities.euler-smooth-r3","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"For an ideal fluid with no viscosity, it is unknown whether a smooth flow filling all of space can concentrate its rotation into infinite values in finite time. Blowup is proven when the fluid touches a wall or when the starting flow is slightly rough.","posed_since":"","precise":"Incompressible Euler on $R^3$ (or $T^3$): does there exist smooth finite-energy initial data (e.g. $C_c^{\\infty}$) whose solution satisfies $\\operatorname{integral}_0^T \\mid\\mid \\omega(t)\\mid\\mid_{\\operatorname{inf}} dt = \\infty$ at a finite $T$, with $\\omega = \\operatorname{curl} u$ (Beale-Kato-Majda criterion)? Known: blowup for smooth data in a cylinder with boundary (Chen and Hou, computer-assisted, PNAS 2025) and for $C^{(1,\\alpha)}$ data on $R^3$ (Elgindi, Annals of Mathematics 2021, small $\\alpha$; Cordoba, Martinez-Zoroa and Zheng, Annals of PDE 2025). Answer: a verified construction or a proof of global regularity.","problem_ref":null,"references":"","settled_by":"An independently verified proof, most likely a computer-assisted nonlinear stability estimate around an approximate self-similar profile.","status_note":"Programmatic searches in September 2026 claimed two Euler singularities (as reported by Petrillo and Glimm, arXiv 2609.23868), and Ganeshram, Duruisseaux and Anandkumar (arXiv 2609.10867) posted a candidate self-similar profile on $R^{3}$ at rate $1/2$ with a stability framework but no completed proof; none is independently verified.","title":"Finite-time blowup of 3D Euler from smooth data without 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