{"id":"https://openalex.org/W1980796127","doi":"https://doi.org/10.1142/s0218127410027428","title":"THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER\u2013STOKES EQUATIONS WITH DELAY","display_name":"THREE-DIMENSIONAL SYSTEM OF GLOBALLY MODIFIED NAVIER\u2013STOKES EQUATIONS WITH DELAY","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W1980796127","doi":"https://doi.org/10.1142/s0218127410027428","mag":"1980796127"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127410027428","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410027428","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5085582592","display_name":"Tom\u00e1s Caraballo","orcid":"https://orcid.org/0000-0003-4697-898X"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"TOM\u00c1S CARABALLO","raw_affiliation_strings":["Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084079816","display_name":"Jos\u00e9 Real","orcid":"https://orcid.org/0000-0003-3918-3265"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"JOS\u00c9 REAL","raw_affiliation_strings":["Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. Ecuaciones Diferenciales y An\u00e1lisis Num\u00e9rico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103403392","display_name":"ANTONIO M. M\u00c1RQUEZ","orcid":null},"institutions":[{"id":"https://openalex.org/I95013407","display_name":"Universidad Pablo de Olavide","ror":"https://ror.org/02z749649","country_code":"ES","type":"education","lineage":["https://openalex.org/I95013407"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"ANTONIO M. M\u00c1RQUEZ","raw_affiliation_strings":["Dpto. de Econom\u00eda, M\u00e9todos Cuantitativos e Historia Econ\u00f3mica, Universidad Pablo de Olavide, Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dpto. de Econom\u00eda, M\u00e9todos Cuantitativos e Historia Econ\u00f3mica, Universidad Pablo de Olavide, Sevilla, Spain","institution_ids":["https://openalex.org/I95013407"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6109,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.92502796,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"09","first_page":"2869","last_page":"2883"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.996399998664856,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9958999752998352,"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/pullback-attractor","display_name":"Pullback attractor","score":0.9412986040115356},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8069413304328918},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.779144287109375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7563176155090332},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.6884459257125854},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6223064661026001},{"id":"https://openalex.org/keywords/pullback","display_name":"Pullback","score":0.55221027135849},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5406913161277771},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4271864593029022},{"id":"https://openalex.org/keywords/hagen\u2013poiseuille-flow-from-the-navier\u2013stokes-equations","display_name":"Hagen\u2013Poiseuille flow from the Navier\u2013Stokes equations","score":0.41923922300338745},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.15412703156471252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08390185236930847}],"concepts":[{"id":"https://openalex.org/C2778100799","wikidata":"https://www.wikidata.org/wiki/Q7259416","display_name":"Pullback attractor","level":3,"score":0.9412986040115356},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8069413304328918},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.779144287109375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563176155090332},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.6884459257125854},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6223064661026001},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.55221027135849},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5406913161277771},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4271864593029022},{"id":"https://openalex.org/C66540979","wikidata":"https://www.wikidata.org/wiki/Q869854","display_name":"Hagen\u2013Poiseuille flow from the Navier\u2013Stokes equations","level":4,"score":0.41923922300338745},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.15412703156471252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08390185236930847},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127410027428","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127410027428","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:dnet:idus________::3e1421ba05af4447803c0f78c5b0e142","is_oa":false,"landing_page_url":"https://idus.us.es/handle/11441/24725","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W192421812","https://openalex.org/W1570440531","https://openalex.org/W1594927479","https://openalex.org/W1768018140","https://openalex.org/W1980798783","https://openalex.org/W1995639579","https://openalex.org/W2035776378","https://openalex.org/W2064959647","https://openalex.org/W2078044459","https://openalex.org/W2147832794","https://openalex.org/W2315114138","https://openalex.org/W2477040106","https://openalex.org/W2477357932","https://openalex.org/W2497754766","https://openalex.org/W2509466248","https://openalex.org/W2515914338","https://openalex.org/W2596083410","https://openalex.org/W3091814460","https://openalex.org/W3103677174","https://openalex.org/W3148800415","https://openalex.org/W4211202937","https://openalex.org/W4250087930"],"related_works":["https://openalex.org/W2056812199","https://openalex.org/W1980810096","https://openalex.org/W2780060059","https://openalex.org/W2963854979","https://openalex.org/W2329905548","https://openalex.org/W2123187692","https://openalex.org/W2533027209","https://openalex.org/W2479468589","https://openalex.org/W1980796127","https://openalex.org/W2951970167"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,21,31],"existence":[3,32],"and":[4,30],"uniqueness":[5],"of":[6,9,13,28,33],"strong":[7],"solutions":[8],"a":[10],"three-dimensional":[11],"system":[12],"globally":[14],"modified":[15],"Navier\u2013Stokes":[16],"equations":[17],"with":[18],"delay":[19],"in":[20],"locally":[22],"Lipschitz":[23],"case.":[24],"The":[25],"asymptotic":[26],"behavior":[27],"solutions,":[29],"pullback":[34],"attractor":[35],"are":[36],"also":[37],"analyzed.":[38]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}