{"id":"https://openalex.org/W3137631502","doi":"https://doi.org/10.1007/s00332-021-09687-4","title":"Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl","display_name":"Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl","publication_year":2021,"publication_date":"2021-03-11","ids":{"openalex":"https://openalex.org/W3137631502","doi":"https://doi.org/10.1007/s00332-021-09687-4","mag":"3137631502"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-021-09687-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-021-09687-4","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016812181","display_name":"Quansen Jiu","orcid":null},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quansen Jiu","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People\u2019s Republic of China","School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People\u2019s Republic of China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People's Republic of China","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101885016","display_name":"Jitao Liu","orcid":"https://orcid.org/0000-0002-6409-1146"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jitao Liu","raw_affiliation_strings":["College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, People\u2019s Republic of China","College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-6409-1146","affiliations":[{"raw_affiliation_string":"College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079247119","display_name":"Dongjuan Niu","orcid":"https://orcid.org/0000-0001-6910-6127"},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongjuan Niu","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People\u2019s Republic of China","School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People\u2019s Republic of China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, People's Republic of China","institution_ids":["https://openalex.org/I96852419"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101885016"],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.6499,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81837472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"31","issue":"2","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9869999885559082,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9796000123023987,"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/euler-equations","display_name":"Euler equations","score":0.7108702063560486},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.704339325428009},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6481727957725525},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5739608407020569},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.5294349193572998},{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"Rotational symmetry","score":0.5265277624130249},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4635794162750244},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.44251886010169983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4368608593940735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41114944219589233},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.3395422697067261},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1211678683757782},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.06864923238754272}],"concepts":[{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.7108702063560486},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.704339325428009},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6481727957725525},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5739608407020569},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5294349193572998},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.5265277624130249},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4635794162750244},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44251886010169983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4368608593940735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41114944219589233},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.3395422697067261},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1211678683757782},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.06864923238754272},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-021-09687-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-021-09687-4","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4000000059604645}],"awards":[{"id":"https://openalex.org/G2001684870","display_name":null,"funder_award_id":"11471220","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2790418368","display_name":null,"funder_award_id":"11671273","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2895501785","display_name":null,"funder_award_id":"11931010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4176582792","display_name":null,"funder_award_id":"11871046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4445510819","display_name":null,"funder_award_id":"1192001","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G5432051516","display_name":null,"funder_award_id":"11801018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8839986861","display_name":null,"funder_award_id":"006000514120513","funder_id":"https://openalex.org/F4320321913","funder_display_name":"Beijing University of Technology"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321913","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1509925099","https://openalex.org/W1612472896","https://openalex.org/W1972995109","https://openalex.org/W1974678251","https://openalex.org/W1988156729","https://openalex.org/W1993502067","https://openalex.org/W2001192987","https://openalex.org/W2016172499","https://openalex.org/W2021619188","https://openalex.org/W2022064238","https://openalex.org/W2024268858","https://openalex.org/W2027147433","https://openalex.org/W2028525992","https://openalex.org/W2036442457","https://openalex.org/W2038013478","https://openalex.org/W2047793620","https://openalex.org/W2052424731","https://openalex.org/W2053188554","https://openalex.org/W2055021661","https://openalex.org/W2073907696","https://openalex.org/W2087742667","https://openalex.org/W2124950677","https://openalex.org/W2152682972","https://openalex.org/W2153252081","https://openalex.org/W2169207127","https://openalex.org/W2244238598","https://openalex.org/W2301372270","https://openalex.org/W2329975672","https://openalex.org/W2558837523","https://openalex.org/W2586989456","https://openalex.org/W2726520144","https://openalex.org/W2806178507","https://openalex.org/W2963145159","https://openalex.org/W2963173588","https://openalex.org/W3103175234","https://openalex.org/W4231892786"],"related_works":["https://openalex.org/W2153510147","https://openalex.org/W4385681600","https://openalex.org/W2165279409","https://openalex.org/W1970898456","https://openalex.org/W1643467562","https://openalex.org/W2029030586","https://openalex.org/W3134117708","https://openalex.org/W2066021295","https://openalex.org/W4384828057","https://openalex.org/W2563697776"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}