{"id":"https://openalex.org/W1988691337","doi":"https://doi.org/10.1007/s00332-004-0648-3","title":"Periodic Structure of 2-D Navier-Stokes Equations","display_name":"Periodic Structure of 2-D Navier-Stokes Equations","publication_year":2005,"publication_date":"2005-05-06","ids":{"openalex":"https://openalex.org/W1988691337","doi":"https://doi.org/10.1007/s00332-004-0648-3","mag":"1988691337"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-004-0648-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-004-0648-3","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/A5101807830","display_name":"Tian Ma","orcid":"https://orcid.org/0000-0003-2062-4884"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]},{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"T. Ma","raw_affiliation_strings":["Department of Mathematics, Sichuan University, Chengdu, P. R. China and Department of Mathematics, Indiana University, Bloomington, IN 47405, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sichuan University, Chengdu, P. R. China and Department of Mathematics, Indiana University, Bloomington, IN 47405, USA","institution_ids":["https://openalex.org/I4210119109","https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037139194","display_name":"S. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"S. Wang","raw_affiliation_strings":["Department of Mathematics, Indiana University, Bloomington, IN 47405, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indiana University, Bloomington, IN 47405, USA","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037139194"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.9403,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69768549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"3","first_page":"133","last_page":"158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9976999759674072,"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":0.9976999759674072,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9969000220298767,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6962125301361084},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6702626943588257},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.5866174101829529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5803943276405334},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5442633032798767},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.5123225450515747},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4451064467430115},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.2683057188987732},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2658762037754059},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.11057555675506592}],"concepts":[{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6962125301361084},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6702626943588257},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5866174101829529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5803943276405334},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5442633032798767},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.5123225450515747},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4451064467430115},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.2683057188987732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2658762037754059},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.11057555675506592},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-004-0648-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-004-0648-3","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W48894704","https://openalex.org/W585983495","https://openalex.org/W1514793153","https://openalex.org/W2020812933","https://openalex.org/W2036631575","https://openalex.org/W2038305321","https://openalex.org/W2085742756","https://openalex.org/W2087057984","https://openalex.org/W2089876099","https://openalex.org/W2127805891","https://openalex.org/W2138904017","https://openalex.org/W2313378072","https://openalex.org/W2328512274","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2971214053","https://openalex.org/W2021517900","https://openalex.org/W2949231297","https://openalex.org/W2060606417","https://openalex.org/W2045623209","https://openalex.org/W13367279","https://openalex.org/W152327667","https://openalex.org/W2243116742","https://openalex.org/W3010480982","https://openalex.org/W2328967475"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
