{"paper":{"title":"Self-focusing of helicity drives finite-time singularities in inviscid flows","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"Helicity self-focuses inside a shrinking tube to create finite-time singularities in inviscid flows.","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Mokhtar Adda-Bedia, Sergio Rica","submitted_at":"2026-05-17T17:58:39Z","abstract_excerpt":"This paper deals with the longstanding quest of the possible existence of finite-time singularities in the equations governing the dynamics of inviscid fluids, namely, Euler equations. Here, two contributions are brought for the case of perfect fluids with finite initial energy. First, a self-similar velocity field inspired by Leray Ansatz is proposed which allows for a separation of variables that transforms the original partial differential Euler equations to a nonlinear system of ordinary differential equations. This system can be solved semi-analytically and allows a continuum set of solut"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We find that the helicity is the driving mechanism of the blow-up through a self-focusing mechanism. The flow near the singularity separates into two phases. A first phase is within a tubular region that shrinks as a power-law (t_c-t)^ν, with t_c the blow-up time, where the helicity is focused. This region is separated by a sharp interface from an outer region where the vorticity, and thus helicity, is identically zero.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that a Leray-inspired self-similar velocity field permits an exact separation of variables that reduces the full Euler PDEs to a closed nonlinear ODE system whose solutions accurately capture the local structure of any actual finite-time singularity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Helicity self-focusing in a power-law shrinking tube drives finite-time singularities in Euler flows, yielding point-like or line-like blow-ups whose exponents are selected by conservation laws.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Helicity self-focuses inside a shrinking tube to create finite-time singularities in inviscid flows.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1e70f220d395c18cdf6f416895a4053b79b5cdc0a566b85bd80804057cfed1e5"},"source":{"id":"2605.17569","kind":"arxiv","version":1},"verdict":{"id":"296a6d2b-bc47-4163-b4c5-4d16f30e2719","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:22:03.358347Z","strongest_claim":"We find that the helicity is the driving mechanism of the blow-up through a self-focusing mechanism. The flow near the singularity separates into two phases. A first phase is within a tubular region that shrinks as a power-law (t_c-t)^ν, with t_c the blow-up time, where the helicity is focused. This region is separated by a sharp interface from an outer region where the vorticity, and thus helicity, is identically zero.","one_line_summary":"Helicity self-focusing in a power-law shrinking tube drives finite-time singularities in Euler flows, yielding point-like or line-like blow-ups whose exponents are selected by conservation laws.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that a Leray-inspired self-similar velocity field permits an exact separation of variables that reduces the full Euler PDEs to a closed nonlinear ODE system whose solutions accurately capture the local structure of any actual finite-time singularity.","pith_extraction_headline":"Helicity self-focuses inside a shrinking tube to create finite-time singularities in inviscid flows."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17569/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.569283Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:31:05.855728Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.596184Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.527711Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"76508fd47a2d9270dd3be6ac815f3a7c57330de5e9755606a4cd948204ed591b"},"references":{"count":32,"sample":[{"doi":"","year":2023,"title":"Amauger, J. , Josserand, C. , Pomeau, Y. & Rica, S. 2023 Two dimensional singularity turbulence . Physica D: Nonlinear Phenomena 443 , 133532","work_id":"34d7311f-a8f6-40df-8704-e7227e72ad5b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Anderson, J. D. 1995 Computational Fluid Dynamics: The Basics with Applications\\/ . McGraw-Hill","work_id":"6c805ad1-36ee-4e36-ba77-11033975959b","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"Barenblatt, G. I. 1996 Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics\\/ . Cambridge University Press","work_id":"4f546aaf-adaa-46e3-911d-3e0caef36f65","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"2020 A fluid mechanic's analysis of the teacup singularity","work_id":"94259283-ab58-4746-af48-624059a35df2","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"Brachet, M. E. 1991 Direct simulation of three-dimensional turbulence in the T aylor- G reen vortex . Fluid Dynamics Research 8 (1), 1--8","work_id":"a8bcc2c9-1c59-44cc-9fa6-c4ba916189cd","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"e45d4521133a7c1d7fd92d7fdbd01a67f211ef3f517b6b6b62876b11a6317343","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"183068fb0144f7936e9235715eba5fba6a5a9e37a2d3c252d3faca2c23ca9ed8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}