{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7c5c8b706e7ce051b17824146ddad00c6cb82ee28e8a7383a115c4793ac302f4","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["12bac92a004b75eefb9a746d6ca32c9f5e10d2704d0c9401a137872fc72dc7d1","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"809a44829a7e775e5d67aee39594db09c11b451f66886df1e1647798db20b618","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"mathph.fluid-singularities.sqg-blowup","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"The surface quasi-geostrophic equation describes temperature carried by a flow it drives itself, and it behaves like a two-dimensional version of the 3D Euler equations. Whether a smooth temperature pattern can form an infinitely sharp front in finite time is unknown.","posed_since":"1994","precise":"Inviscid SQG: $\\mathrm{d}\\theta/\\mathrm{d}t + u . \\mathrm{grad}\\,\\theta = 0$, $u = (-R_2 \\theta, R_1 \\theta)$ with $R_j$ the Riesz transforms, on $R^2$ or $T^2$, smooth (e.g. $C_c^\\infty$) initial $\\theta$, no forcing. Prove global regularity, or give smooth data with $\\int_{0}^{T} ||\\mathrm{grad}\\,\\theta(t)||_{\\mathrm{inf}}\\,\\mathrm{d}t = \\infty$ at finite T. Answer: yes or no with proof.","problem_ref":"12bac92a004b75eefb9a746d6ca32c9f5e10d2704d0c9401a137872fc72dc7d1","references":"","settled_by":"A proof of global regularity or a verified finite-time singularity from smooth finite-energy data without forcing.","status_note":"Frontal blowup was proposed by Constantin, Majda and Tabak (1994); blowup from smooth compactly supported data with a suitable time-dependent force, inside the Sobolev well-posedness regime, was proven for generalized SQG with $\\gamma \\text{ in } (0,1)$ (Cordoba, Dominguez, Lucas-Manchon and Martinez-Zoroa, arXiv 2608.17192, 2026), not for unforced SQG.","title":"Finite-time singularity of the inviscid surface quasi-geostrophic equation","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"faf187a54bae6eb8389b51e836f9ccd9752b904a8719968012b0a72239b43907","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f02125cc145b1ae2b6faf0988e4acb83e48c9ea53048e91d9fc6939c9ec71f46","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"OLNHQjh-thh_woQoazV77sLLRdqJ_w4wPaf6H0UaXpy-n-IGq6dAecTeHyQpQqolTcw5y6Mw6ZJuNJOSfAGzCg"},"schema":"pubphys.envelope/1"},"record_hash":"faf187a54bae6eb8389b51e836f9ccd9752b904a8719968012b0a72239b43907","leaf_index":3420}