{"id":"https://openalex.org/W7133339022","doi":"https://doi.org/10.48550/arxiv.2603.01600","title":"Analysis of Robin-boundary control for the Boussinesq equations","display_name":"Analysis of Robin-boundary control for the Boussinesq equations","publication_year":2026,"publication_date":"2026-03-02","ids":{"openalex":"https://openalex.org/W7133339022","doi":"https://doi.org/10.48550/arxiv.2603.01600"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.01600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01600","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.01600","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127981212","display_name":"Wei Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127976874","display_name":"Dongdong Liang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liang, Dongdong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043528294","display_name":"Xianbing Luo","orcid":"https://orcid.org/0000-0003-0414-7504"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Xianbing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007836867","display_name":"Changlun Ye","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ye, Changlun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7997999787330627,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7997999787330627,"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":0.08330000191926956,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.04280000180006027,"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/discretization","display_name":"Discretization","score":0.7631999850273132},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6807000041007996},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5044000148773193},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4659999907016754},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.42910000681877136},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4074999988079071},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.36480000615119934},{"id":"https://openalex.org/keywords/adjoint-equation","display_name":"Adjoint equation","score":0.3637000024318695},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3589000105857849}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7631999850273132},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6807000041007996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6775000095367432},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5336999893188477},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5044000148773193},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4659999907016754},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.42910000681877136},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3749000132083893},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.36480000615119934},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.3637000024318695},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C97985569","wikidata":"https://www.wikidata.org/wiki/Q216861","display_name":"Calculus of variations","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3111000061035156},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C181152433","wikidata":"https://www.wikidata.org/wiki/Q895274","display_name":"Boussinesq approximation (buoyancy)","level":5,"score":0.29750001430511475},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.01600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01600","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.01600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.01600","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,70],"study":[4],"an":[5],"optimal":[6,67],"boundary":[7,31],"control":[8,26,112],"problem":[9,44],"for":[10,96,106],"the":[11,16,25,39,42,62,66,97,107],"Boussinesq":[12],"equations,":[13],"which":[14],"couple":[15],"time-dependent":[17],"Navier-Stokes":[18],"system":[19],"with":[20,93],"a":[21,29,46,72,77,87,102],"heat":[22],"equation,":[23],"where":[24],"enters":[27],"through":[28],"Robin":[30],"condition":[32],"on":[33],"temperature.":[34],"We":[35,49,99],"begin":[36],"by":[37],"establishing":[38],"well-posedness":[40],"of":[41,61,76],"optimization":[43],"via":[45],"variational":[47,94],"framework.":[48],"then":[50],"derive":[51],"both":[52],"first-":[53],"and":[54,65,86,111],"second-order":[55],"optimality":[56],"conditions,":[57],"including":[58],"explicit":[59],"characterizations":[60],"adjoint":[63,109],"state":[64],"control.":[68,98],"Next,":[69],"perform":[71],"detailed":[73],"numerical":[74],"analysis":[75],"fully":[78],"discrete":[79],"scheme:":[80],"using":[81],"finite":[82],"elements":[83],"in":[84,90],"space":[85],"semi-implicit":[88],"scheme":[89],"time,":[91],"combined":[92],"discretization":[95],"present":[100],"rigorous":[101],"prior":[103],"error":[104],"estimates":[105],"state,":[108,110],"variables.":[113],"Numerical":[114],"experiments":[115],"are":[116],"provided":[117],"to":[118],"validate":[119],"our":[120],"theoretical":[121],"results.":[122]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-04T00:00:00"}