{"id":"https://openalex.org/W1981143400","doi":"https://doi.org/10.1137/110837164","title":"Stabilization of Navier--Stokes Equations by Oblique Boundary Feedback Controllers","display_name":"Stabilization of Navier--Stokes Equations by Oblique Boundary Feedback Controllers","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1981143400","doi":"https://doi.org/10.1137/110837164","mag":"1981143400"},"language":"en","primary_location":{"id":"doi:10.1137/110837164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110837164","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1106.3931","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Viorel Barbu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102862771"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7045,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85684059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"4","first_page":"2288","last_page":"2307"},"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":0.9995999932289124,"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":0.9995999932289124,"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":0.9879999756813049,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9843000173568726,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/oblique-case","display_name":"Oblique case","score":0.8463903665542603},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5994054675102234},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5782723426818848},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5220189690589905},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.38496387004852295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37761732935905457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36121973395347595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35833311080932617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3436439037322998},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2581877112388611},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.04147055745124817}],"concepts":[{"id":"https://openalex.org/C160697094","wikidata":"https://www.wikidata.org/wiki/Q1233197","display_name":"Oblique case","level":2,"score":0.8463903665542603},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5994054675102234},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5782723426818848},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5220189690589905},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.38496387004852295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37761732935905457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36121973395347595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35833311080932617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3436439037322998},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2581877112388611},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.04147055745124817},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/110837164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110837164","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:1106.3931","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.3931","pdf_url":"https://arxiv.org/pdf/1106.3931","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1981143400","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1106.3931","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1106.3931","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1106.3931","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1106.3931","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1106.3931","pdf_url":"https://arxiv.org/pdf/1106.3931","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1981143400.pdf","grobid_xml":"https://content.openalex.org/works/W1981143400.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W21855041","https://openalex.org/W1570440531","https://openalex.org/W1967563465","https://openalex.org/W1969286983","https://openalex.org/W1979079822","https://openalex.org/W1991675143","https://openalex.org/W1995578325","https://openalex.org/W1997362851","https://openalex.org/W2005266531","https://openalex.org/W2006101334","https://openalex.org/W2015445411","https://openalex.org/W2017352803","https://openalex.org/W2020303008","https://openalex.org/W2027184764","https://openalex.org/W2030140685","https://openalex.org/W2056065957","https://openalex.org/W2059125206","https://openalex.org/W2079545658","https://openalex.org/W2088923946","https://openalex.org/W2117782033","https://openalex.org/W2119597296","https://openalex.org/W2161631852","https://openalex.org/W2163972713","https://openalex.org/W2319765174","https://openalex.org/W2963021809","https://openalex.org/W4245502469"],"related_works":["https://openalex.org/W2044049625","https://openalex.org/W251271928","https://openalex.org/W2505036030","https://openalex.org/W1969286983","https://openalex.org/W2054292840","https://openalex.org/W2088923946","https://openalex.org/W2963012987","https://openalex.org/W2478368202","https://openalex.org/W2963015277","https://openalex.org/W2063648462","https://openalex.org/W1982766233","https://openalex.org/W2767123409","https://openalex.org/W2484279510","https://openalex.org/W2014453968","https://openalex.org/W1977247921","https://openalex.org/W2002234046","https://openalex.org/W2795391692","https://openalex.org/W1978521281","https://openalex.org/W3025045705","https://openalex.org/W1838017358"],"abstract_inverted_index":{"One":[0],"designs":[1],"a":[2,17,31],"linear":[3],"stabilizing":[4],"boundary":[5,36],"feedback":[6],"controller":[7,87],"$u$":[8],"for":[9,55],"the":[10,35,41,51,56,63,69,89],"equilibrium":[11],"solutions":[12],"to":[13,50,65],"Navier--Stokes":[14],"system":[15,53],"on":[16,82],"bounded":[18],"and":[19,38,73],"open":[20],"domain":[21],"$\\mathcal{O}\\subset\\mathbb{R}^d,":[22],"d=2$,":[23],"$u=\\eta\\mbox{$1\\!\\!\\!\\;\\mathrml$}_\\Gamma\\displaystyle\\sum\\nolimits^N_{j=1}\\mu_j\\left<y,\\varphi^*_j\\right>":[24],"(\\phi_j":[25],"(x)+\\alpha(x)\\vec":[26],"n(x))$,":[27],"where":[28],"$\\Gamma$":[29],"is":[30,40,62,68,75],"connected":[32],"component":[33],"of":[34,44],"$\\partial\\mathcal{O}$":[37],"$\\mbox{$1\\!\\!\\!\\;\\mathrml$}_\\Gamma$":[39],"characteristic":[42],"function":[43],"$\\Gamma$.":[45],"Here,":[46],"$\\phi_j$":[47],"are":[48],"related":[49],"eigenfunction":[52],"$\\{\\varphi^*_j\\}$":[54],"adjoint":[57],"Stokes--Oseen":[58],"system,":[59],"$\\vec":[60],"n$":[61],"normal":[64],"$\\partial\\mathcal{O}$,":[66],"$\\left<\\cdot,\\cdot\\right>$":[67],"scalar":[70],"product":[71],"in$(L^2(\\mathcal{O}))^d$,":[72],"$\\alpha$":[74],"an":[76],"arbitrary":[77],"$C^2$-function":[78],"with":[79],"circulation":[80],"zero":[81],"$\\partial\\mathcal{O}$.":[83],"For":[84],"$d=2,3$":[85],"this":[86],"stabilizes":[88],"corresponding":[90],"linearized":[91],"(Oseen--Stokes)":[92],"system.":[93]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
