{"id":"https://openalex.org/W3045846440","doi":"https://doi.org/10.1137/18m117652x","title":"Observability Inequalities on Measurable Sets for the Stokes System and Applications","display_name":"Observability Inequalities on Measurable Sets for the Stokes System and Applications","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3045846440","doi":"https://doi.org/10.1137/18m117652x","mag":"3045846440"},"language":"en","primary_location":{"id":"doi:10.1137/18m117652x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m117652x","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":["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/A5046964322","display_name":"Felipe W. Chaves-Silva","orcid":"https://orcid.org/0000-0002-4350-4773"},"institutions":[{"id":"https://openalex.org/I169045520","display_name":"Universidade Federal da Para\u00edba","ror":"https://ror.org/00p9vpz11","country_code":"BR","type":"education","lineage":["https://openalex.org/I169045520"]},{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["BR","CN"],"is_corresponding":false,"raw_author_name":"Felipe W. Chaves-Silva","raw_affiliation_strings":["\\dagger Department of Mathematics, Federal University of Para\\' {\\i} ba, UFPB, CEP 58051-900, Jo\\\u00e3o Pessoa, PB, Brazil","School of Mathematics and Statistics, Wuhan University; Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China","\\ddagger Department of Mathematics, Federal University of Pernambuco, CEP 50740-545, Recife, PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-4350-4773","affiliations":[{"raw_affiliation_string":"\\dagger Department of Mathematics, Federal University of Para\\' {\\i} ba, UFPB, CEP 58051-900, Jo\\\u00e3o Pessoa, PB, Brazil","institution_ids":["https://openalex.org/I169045520"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University; Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, Federal University of Pernambuco, CEP 50740-545, Recife, PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017946369","display_name":"Diego A. Souza","orcid":"https://orcid.org/0000-0001-7763-8174"},"institutions":[{"id":"https://openalex.org/I169045520","display_name":"Universidade Federal da Para\u00edba","ror":"https://ror.org/00p9vpz11","country_code":"BR","type":"education","lineage":["https://openalex.org/I169045520"]},{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]},{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["BR","CN"],"is_corresponding":false,"raw_author_name":"Diego A. Souza","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University; Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China","\\dagger Department of Mathematics, Federal University of Para\\' {\\i} ba, UFPB, CEP 58051-900, Jo\\\u00e3o Pessoa, PB, Brazil","\\ddagger Department of Mathematics, Federal University of Pernambuco, CEP 50740-545, Recife, PE, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-7763-8174","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University; Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China","institution_ids":["https://openalex.org/I37461747"]},{"raw_affiliation_string":"\\dagger Department of Mathematics, Federal University of Para\\' {\\i} ba, UFPB, CEP 58051-900, Jo\\\u00e3o Pessoa, PB, Brazil","institution_ids":["https://openalex.org/I169045520"]},{"raw_affiliation_string":"\\ddagger Department of Mathematics, Federal University of Pernambuco, CEP 50740-545, Recife, PE, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100440846","display_name":"Can Zhang","orcid":"https://orcid.org/0000-0003-3118-8379"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Can Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.083873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"58","issue":"4","first_page":"2188","last_page":"2205"},"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":0.9952999949455261,"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":0.9952999949455261,"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":0.9886999726295471,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9620000123977661,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8295096755027771},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.8271284103393555},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7086004614830017},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.6824617385864258},{"id":"https://openalex.org/keywords/measurable-function","display_name":"Measurable function","score":0.4434276521205902},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.42658519744873047},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40797337889671326},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3737097382545471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3630750775337219},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3275170624256134},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.23900192975997925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23579749464988708},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08157098293304443}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8295096755027771},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.8271284103393555},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7086004614830017},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.6824617385864258},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.4434276521205902},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.42658519744873047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40797337889671326},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3737097382545471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3630750775337219},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3275170624256134},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.23900192975997925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23579749464988708},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08157098293304443},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m117652x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m117652x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6200000047683716}],"awards":[{"id":"https://openalex.org/G1123707339","display_name":null,"funder_award_id":"88881.311964/2018-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G116629194","display_name":null,"funder_award_id":"88881","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G1282811550","display_name":null,"funder_award_id":"2019/0014","funder_id":"https://openalex.org/F4320323351","funder_display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Estado da Para\u00edba"},{"id":"https://openalex.org/G1284542019","display_name":null,"funder_award_id":"2019/0014","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G1460313966","display_name":"From Open to Closed Loop Optimal Control of PDEs","funder_award_id":"668998","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G1913932332","display_name":null,"funder_award_id":"2018-01","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2734491381","display_name":null,"funder_award_id":"ERC-2012-ADG","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G5078064498","display_name":null,"funder_award_id":"11971363","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5229793628","display_name":null,"funder_award_id":"2042019kf0023","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5456659865","display_name":null,"funder_award_id":"2018-01","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G6707245813","display_name":null,"funder_award_id":"11771344","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6815844370","display_name":null,"funder_award_id":"88881","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6828757805","display_name":null,"funder_award_id":"413100085","funder_id":"https://openalex.org/F4320324116","funder_display_name":"Wuhan University"},{"id":"https://openalex.org/G8580170231","display_name":null,"funder_award_id":"668998","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323351","display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Estado da Para\u00edba","ror":"https://ror.org/021y4b202"},{"id":"https://openalex.org/F4320324116","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17"},{"id":"https://openalex.org/F4320324901","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335213","display_name":"Pr\u00f3-Reitoria de Pesquisa, Universidade Federal do Rio Grande do Sul","ror":"https://ror.org/041yk2d64"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W775933467","https://openalex.org/W1179366910","https://openalex.org/W1980190132","https://openalex.org/W1984052922","https://openalex.org/W1991288696","https://openalex.org/W2011483362","https://openalex.org/W2027290972","https://openalex.org/W2043233479","https://openalex.org/W2054306329","https://openalex.org/W2066164065","https://openalex.org/W2068603868","https://openalex.org/W2137660413","https://openalex.org/W2139492487","https://openalex.org/W2161909192","https://openalex.org/W2171568556","https://openalex.org/W2417862190","https://openalex.org/W2625273684","https://openalex.org/W2963551263","https://openalex.org/W2963576390","https://openalex.org/W2964171923","https://openalex.org/W3102383043"],"related_works":["https://openalex.org/W2027310873","https://openalex.org/W224232026","https://openalex.org/W4226192090","https://openalex.org/W2074721578","https://openalex.org/W4297812948","https://openalex.org/W2403901226","https://openalex.org/W2003094584","https://openalex.org/W2033574161","https://openalex.org/W4300106302","https://openalex.org/W105766698"],"abstract_inverted_index":{"In":[0,91],"this":[1],"paper,":[2],"we":[3,70,93],"establish":[4],"spectral":[5],"inequalities":[6,22],"on":[7,23],"measurable":[8,25],"sets":[9,26],"of":[10,27,56,60],"positive":[11,28,61,96],"Lebesgue":[12],"measure":[13,29,62],"for":[14,30,87],"the":[15,37,54,75,82,88],"Stokes":[16,32,89],"operator,":[17],"as":[18,20,79,81],"well":[19,80],"observability":[21],"space-time":[24],"nonstationary":[31],"system.":[33,90],"The":[34],"latter":[35],"extends":[36],"result":[38],"established":[39],"recently":[40],"by":[41,103],"Wang":[42],"and":[43,66,106],"Zhang":[44],"[SIAM":[45],"J.":[46],"Control":[47],"Optim.,":[48],"55":[49],"(2017),":[50],"pp.":[51,114],"1862--1886]":[52],"to":[53,98],"case":[55],"observations":[57],"from":[58],"subsets":[59],"in":[63,74],"both":[64],"time":[65,83],"space":[67],"variables.":[68],"Furthermore,":[69],"present":[71],"their":[72],"applications":[73],"shape":[76],"optimization":[77],"problem,":[78],"optimal":[84],"control":[85],"problem":[86],"particular,":[92],"give":[94],"a":[95],"answer":[97],"an":[99],"open":[100],"question":[101],"raised":[102],"Privat,":[104],"Tr\u00e9lat,":[105],"Zuazua":[107],"[Arch.":[108],"Rational":[109],"Mech.":[110],"Anal.,":[111],"216":[112],"(2015),":[113],"921--981].":[115]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}