{"id":"https://openalex.org/W2100524240","doi":"https://doi.org/10.1137/100785739","title":"Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier\u2013Stokes Equations","display_name":"Internal Exponential Stabilization to a Nonstationary Solution for 3D Navier\u2013Stokes Equations","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2100524240","doi":"https://doi.org/10.1137/100785739","mag":"2100524240"},"language":"en","primary_location":{"id":"doi:10.1137/100785739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100785739","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1002.2176","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102862771","display_name":"Viorel Barbu","orcid":"https://orcid.org/0000-0002-4715-9778"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Viorel Barbu","raw_affiliation_strings":["\u2018Alexandru Ioan Cuza\u2019 University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2018Alexandru Ioan Cuza\u2019 University","institution_ids":["https://openalex.org/I138164181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029809063","display_name":"S\u00e9rgio S. Rodrigues","orcid":"https://orcid.org/0000-0002-4604-4856"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"S\u00e9rgio S. Rodrigues","raw_affiliation_strings":["Austrian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Austrian Academy of Sciences","institution_ids":["https://openalex.org/I138211613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026354657","display_name":"Armen Shirikyan","orcid":"https://orcid.org/0000-0003-2535-844X"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Armen Shirikyan","raw_affiliation_strings":["Austrian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Austrian Academy of Sciences","institution_ids":["https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2571,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.95429993,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"49","issue":"4","first_page":"1454","last_page":"1478"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.955299973487854,"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/mathematics","display_name":"Mathematics","score":0.8709105253219604},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.6961580514907837},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6597315073013306},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5826188325881958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5717880725860596},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5619208812713623},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5037898421287537},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4410207271575928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4003527760505676}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8709105253219604},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.6961580514907837},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6597315073013306},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5826188325881958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5717880725860596},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5619208812713623},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5037898421287537},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4410207271575928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4003527760505676},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/100785739","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100785739","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1002.2176","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.2176","pdf_url":"https://arxiv.org/pdf/1002.2176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.770.7500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.770.7500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1002.2176.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00455250v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00455250","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2010","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1002.2176","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1002.2176","pdf_url":"https://arxiv.org/pdf/1002.2176","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W630764638","https://openalex.org/W1466924688","https://openalex.org/W1493492050","https://openalex.org/W1499788862","https://openalex.org/W1604226557","https://openalex.org/W1969286983","https://openalex.org/W1969989456","https://openalex.org/W2015445411","https://openalex.org/W2030140685","https://openalex.org/W2043233479","https://openalex.org/W2056065957","https://openalex.org/W2059125206","https://openalex.org/W2075432230","https://openalex.org/W2076582418","https://openalex.org/W2077687987","https://openalex.org/W2088923946","https://openalex.org/W2119597296","https://openalex.org/W2151032208","https://openalex.org/W2315917513","https://openalex.org/W2956143396","https://openalex.org/W3091814460","https://openalex.org/W4245502469"],"related_works":["https://openalex.org/W2046459260","https://openalex.org/W2967463586","https://openalex.org/W2765830098","https://openalex.org/W1971989957","https://openalex.org/W3157641275","https://openalex.org/W2154600465","https://openalex.org/W2964287305","https://openalex.org/W3107918277","https://openalex.org/W2431947387","https://openalex.org/W4306823219"],"abstract_inverted_index":{"We":[0,67],"consider":[1],"the":[2,36,51,55,63,71,75,81],"Navier\u2013Stokes":[3,83],"system":[4],"in":[5],"a":[6,10,14,22,30,47],"bounded":[7],"domain":[8],"with":[9],"smooth":[11],"boundary.":[12],"Given":[13],"sufficiently":[15],"regular":[16],"time-dependent":[17],"global":[18],"solution,":[19],"we":[20],"construct":[21],"finite-dimensional":[23],"feedback":[24],"control":[25,65,72],"that":[26,70],"is":[27,44],"supported":[28],"by":[29],"given":[31],"open":[32],"set":[33],"and":[34,58],"stabilizes":[35,78],"linearized":[37,56],"equation.":[38],"The":[39],"proof":[40],"of":[41,62],"this":[42],"fact":[43],"based":[45],"on":[46],"truncated":[48],"observability":[49],"inequality,":[50],"regularizing":[52],"property":[53],"for":[54,74],"equation,":[57],"some":[59],"standard":[60],"techniques":[61],"optimal":[64],"theory.":[66],"then":[68],"show":[69],"constructed":[73],"linear":[76],"problem":[77],"locally":[79],"also":[80],"full":[82],"system.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
