{"id":"https://openalex.org/W3016090278","doi":"https://doi.org/10.1007/s00211-022-01333-9","title":"How and why non smooth solutions of the 3D Navier\u2013Stokes equations could possibly develop","display_name":"How and why non smooth solutions of the 3D Navier\u2013Stokes equations could possibly develop","publication_year":2022,"publication_date":"2022-11-10","ids":{"openalex":"https://openalex.org/W3016090278","doi":"https://doi.org/10.1007/s00211-022-01333-9","mag":"3016090278"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-022-01333-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-022-01333-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://iris.unimore.it/bitstream/11380/1291085/2/2004.04262.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042821533","display_name":"Daniele Funaro","orcid":"https://orcid.org/0000-0001-7858-4542"},"institutions":[{"id":"https://openalex.org/I122346577","display_name":"University of Modena and Reggio Emilia","ror":"https://ror.org/02d4c4y02","country_code":"IT","type":"education","lineage":["https://openalex.org/I122346577"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Daniele Funaro","raw_affiliation_strings":["Dipartimento di Scienze Chimiche e Geologiche, Universit\u00e0 di Modena e Reggio Emilia, Via Campi 103, 41125, Modena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze Chimiche e Geologiche, Universit\u00e0 di Modena e Reggio Emilia, Via Campi 103, 41125, Modena, Italy","institution_ids":["https://openalex.org/I122346577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042821533"],"corresponding_institution_ids":["https://openalex.org/I122346577"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00333728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"152","issue":"4","first_page":"789","last_page":"817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9986000061035156,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7424399256706238},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.741560697555542},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.6809154748916626},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.658839225769043},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5456576347351074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45726048946380615},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41546106338500977},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4105875790119171},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19265088438987732},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.1751202642917633},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.15425938367843628},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0966513454914093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7424399256706238},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.741560697555542},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.6809154748916626},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.658839225769043},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5456576347351074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45726048946380615},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41546106338500977},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4105875790119171},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19265088438987732},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.1751202642917633},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.15425938367843628},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0966513454914093},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-022-01333-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-022-01333-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:iris.unimore.it:11380/1291085","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1291085","pdf_url":"https://iris.unimore.it/bitstream/11380/1291085/2/2004.04262.pdf","source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:iris.unimore.it:11380/1291085","is_oa":true,"landing_page_url":"https://hdl.handle.net/11380/1291085","pdf_url":"https://iris.unimore.it/bitstream/11380/1291085/2/2004.04262.pdf","source":{"id":"https://openalex.org/S4306400718","display_name":"IRIS UNIMORE (University of Modena and Reggio Emilia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122346577","host_organization_name":"University of Modena and Reggio Emilia","host_organization_lineage":["https://openalex.org/I122346577"],"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":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3016090278.pdf","grobid_xml":"https://content.openalex.org/works/W3016090278.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W213469731","https://openalex.org/W1560338481","https://openalex.org/W1591373735","https://openalex.org/W1603842336","https://openalex.org/W1884507372","https://openalex.org/W1988761547","https://openalex.org/W1992279042","https://openalex.org/W1996952201","https://openalex.org/W2017700628","https://openalex.org/W2020481939","https://openalex.org/W2021073558","https://openalex.org/W2025151393","https://openalex.org/W2025611614","https://openalex.org/W2041610574","https://openalex.org/W2046528357","https://openalex.org/W2151847866","https://openalex.org/W2570442251","https://openalex.org/W2591824599","https://openalex.org/W2611751909","https://openalex.org/W2788569876","https://openalex.org/W2908131044","https://openalex.org/W2963673628","https://openalex.org/W2973053442","https://openalex.org/W2980325255","https://openalex.org/W2995875170","https://openalex.org/W3106140646","https://openalex.org/W4230778004"],"related_works":["https://openalex.org/W2054384926","https://openalex.org/W2118359714","https://openalex.org/W2562957045","https://openalex.org/W3016090278","https://openalex.org/W3155529219","https://openalex.org/W2313747348","https://openalex.org/W1579334083","https://openalex.org/W654337712","https://openalex.org/W2950851317","https://openalex.org/W1989818238"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-31T08:46:17.908082","created_date":"2025-10-10T00:00:00"}
