{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"30cafa06ccf5afd4d5c9c0f615ff2ddfec33aea49ae3ea763d062be670c7dcd4","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1982624223c8ec9ddf774f84798346cccefd0f93106a472d5bd57ab4cae56738","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.fluid-singularities.sqg-blowup","kind":"well-posed","literature_status":"open","n":"1","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: d theta/dt + u . 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 integral_0^T ||grad theta(t)||_inf dt = infinity at finite T. Answer: yes or no with proof.","problem_ref":null,"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":"56471002f5ad6f04f20e12861588794aa7901ecb598d7f960b48900e00132b59"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"12bac92a004b75eefb9a746d6ca32c9f5e10d2704d0c9401a137872fc72dc7d1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"283b733a3d4293ec15206dfc18b200b064befd17fa48b301fd9daa4d9e090aad","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sVPH85l3a25J1Ccha_a-eB8GlFrFFF_HIWFvNWlu7BvhBd3xARtzjUm6pDUoT0VPGYN-uhHoSQpb4OPaqlywAw"},"schema":"pubphys.envelope/1"},"record_hash":"12bac92a004b75eefb9a746d6ca32c9f5e10d2704d0c9401a137872fc72dc7d1","leaf_index":1621}