{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"fde0334a7b9d63b2823a7817e782ab6685ab2caacb7dd449bb289d653b345208","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"d942ecaeea8f84b272b05c6a11fe4d2495b9e790f72dcfe55a4aa4b0db582ddb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.fluid-singularities.unstable-profiles","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Computer searches in 2025 found self-similar blowup solutions that occur only for finely tuned starting flows (unstable singularities) in simpler 2D fluid models. Turning these numerical profiles into proofs is open.","posed_since":"2025","precise":"Wang et al. (arXiv 2509.14185, 2025) computed families of unstable self-similar profiles to high precision for the Cordoba-Cordoba-Fontelos model, the 2D incompressible porous media equation and the 2D Boussinesq equations with boundary. Prove that at least one such profile yields an exact finite-time singularity from smooth data, by a computer-assisted stability estimate on the finite-codimension set of data attracted to it. Answer: a proof for each profile family.","problem_ref":null,"references":"","settled_by":"A computer-assisted proof of nonlinear stability modulo finitely many unstable directions for one profile of the unforced equations.","status_note":"Profiles were computed numerically in 2025; a rigorous stability proof was the stated next step.","title":"Rigorous unstable self-similar singularities in incompressible fluid models","topic_ref":"56471002f5ad6f04f20e12861588794aa7901ecb598d7f960b48900e00132b59"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"6a7c881708bc312b22d92e3d7fa9d0cbb32dbae9d9bd4efb83c0e6f7353d678c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"793634f0fbde7115cc659f3b0dcceb29a180678ac18bb73799e9581789bdc32c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"eF1tSxY2GrUKZDV2JRHh16feXNnoBAl0AvMOEWv91IUdi5TARDpJXo0yG-4l6SanKA3PtfmHhFHWioWxemr4Dw"},"schema":"pubphys.envelope/1"},"record_hash":"6a7c881708bc312b22d92e3d7fa9d0cbb32dbae9d9bd4efb83c0e6f7353d678c","leaf_index":1622}