{"id":"https://openalex.org/W7211874409","doi":"https://doi.org/10.48550/arxiv.2609.05193","title":"Global well-posedness of the 3D Navier-Stokes equations with helical $L^1$ vorticity","display_name":"Global well-posedness of the 3D Navier-Stokes equations with helical $L^1$ vorticity","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211874409","doi":"https://doi.org/10.48550/arxiv.2609.05193"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05193","pdf_url":"https://arxiv.org/pdf/2609.05193","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.05193","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086926125","display_name":"Francisco Gancedo","orcid":"https://orcid.org/0000-0002-9006-8804","observed_orcids":["https://orcid.org/0000-0002-9006-8804"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gancedo, Francisco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5093367481","display_name":"Antonio Hidalgo-Torn\u00e9","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hidalgo-Torn\u00e9, Antonio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.9300000071525574},{"id":"https://openalex.org/keywords/global-well-posedness","display_name":"global well-posedness","score":0.9909999966621399},{"id":"https://openalex.org/keywords/helical-flow","display_name":"helical flow","score":0.6209999918937683},{"id":"https://openalex.org/keywords/supercriticality","display_name":"supercriticality","score":0.5649999976158142},{"id":"https://openalex.org/keywords/three-dimensional-incompressible-flow","display_name":"three-dimensional incompressible flow","score":0.6740000247955322},{"id":"https://openalex.org/keywords/torus-domain","display_name":"torus domain","score":0.3319999873638153}],"concepts":[{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.7146999835968018},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5412999987602234},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.49129998683929443},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.4668000042438507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3846000134944916},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.32760000228881836},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C162157250","wikidata":"https://www.wikidata.org/wiki/Q3730817","display_name":"Vorticity equation","level":4,"score":0.28790000081062317},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2549999952316284},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05193","pdf_url":"https://arxiv.org/pdf/2609.05193","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.05193","doi":"https://doi.org/10.48550/arxiv.2609.05193","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05193","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.05193","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05193","pdf_url":"https://arxiv.org/pdf/2609.05193","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1175115578","display_name":null,"funder_award_id":"AEI//10.13039/501100011033/","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1243386076","display_name":null,"funder_award_id":"PID2022-140494NA-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G294895050","display_name":null,"funder_award_id":"MICIU/AEI /10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3681338154","display_name":null,"funder_award_id":"RED2022-134784-T","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4025565791","display_name":null,"funder_award_id":"CEX2024-001517-M","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G425668148","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https://ror.org/00ez2he07"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211874409.pdf","grobid_xml":"https://content.openalex.org/works/W7211874409.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4391335922","https://openalex.org/W4416068976"],"related_works":["https://openalex.org/W2558837523","https://openalex.org/W4409353408","https://openalex.org/W2892213087","https://openalex.org/W4313598255","https://openalex.org/W4403419860","https://openalex.org/W4299630923","https://openalex.org/W2083749100","https://openalex.org/W2589557194","https://openalex.org/W4401404611","https://openalex.org/W2316170472"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,17],"the":[3,43,53,56,66],"Navier-Stokes":[4,58],"equations":[5],"on":[6],"$\\mathbb":[7],"R^2\\times\\mathbb":[8],"T$":[9],"are":[10,18],"globally":[11],"well":[12],"posed":[13],"for":[14],"initial":[15],"vorticities":[16],"both":[19],"helically":[20],"symmetric":[21],"and":[22,60],"integrable.":[23],"This":[24,48],"class":[25],"of":[26,32,55,69],"data":[27],"typically":[28],"generates":[29],"velocity":[30],"fields":[31],"infinite":[33],"kinetic":[34],"energy,":[35],"so":[36],"this":[37],"result":[38,49],"is":[39,50,62],"not":[40],"covered":[41],"by":[42,65],"classical":[44],"finite-energy":[45],"well-posedness":[46],"theory.":[47],"supercritical":[51],"from":[52],"perspective":[54],"three-dimensional":[57],"scaling,":[59],"it":[61],"made":[63],"possible":[64],"special":[67],"structure":[68],"helical":[70],"flows":[71],"using":[72],"time-weighted":[73],"Kato-type":[74],"spaces.":[75]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}