{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ea8eeab238db69c37d93c0476f42ea13e427337edcf06ebf67e341f0dd6bc5de","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["8d1f292a7985bab3abd92a1e50818728f04ef1d87ceefb99805d3c7d9863ee85","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"2d5a915ad8d417aa558617874830c40c1ab4655f5f3795e4fe7e90d1aed9634a","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":"2","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 $\\int_0^T \\mid\\mid \\omega(t)\\mid\\mid_{\\operatorname{inf}} dt = \\infty$ 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":"8d1f292a7985bab3abd92a1e50818728f04ef1d87ceefb99805d3c7d9863ee85","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 boundaries","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"4aa92af6f64fc8ede6a500a1197f5bdf02d691f70658b7ce34c84e8d259519f6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f0f50d65adadce370508b5e0553eebf6064955ecc38563fac82e294cd96517fa","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"OX0jbysAsVSiw0mi_AIfIRuj64Xl2H100n6tMxL8GPf3-Za5mbgh5keMKLlXm9G53_4A49XBUmqQYs0TrenTCw"},"schema":"pubphys.envelope/1"},"record_hash":"4aa92af6f64fc8ede6a500a1197f5bdf02d691f70658b7ce34c84e8d259519f6","leaf_index":3414}