{"id":"https://openalex.org/W2012099743","doi":"https://doi.org/10.1137/090758179","title":"Shape Derivative of Drag Functional","display_name":"Shape Derivative of Drag Functional","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2012099743","doi":"https://doi.org/10.1137/090758179","mag":"2012099743"},"language":"en","primary_location":{"id":"doi:10.1137/090758179","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090758179","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/A5081980551","display_name":"\u041f. \u0418. \u041f\u043b\u043e\u0442\u043d\u0438\u043a\u043e\u0432","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. I. Plotnikov","raw_affiliation_strings":["plotnikov@hydro.nsc.ru#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"plotnikov@hydro.nsc.ru#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078359464","display_name":"Jan Soko\u0142owski","orcid":"https://orcid.org/0000-0002-3560-7342"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Sokolowski","raw_affiliation_strings":["Jan.Sokolowski@iecn.u-nancy.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jan.Sokolowski@iecn.u-nancy.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0874,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.91253867,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"48","issue":"7","first_page":"4680","last_page":"4706"},"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":0.9991999864578247,"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":0.9991999864578247,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9987000226974487,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8428688049316406},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6989524960517883},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.656733512878418},{"id":"https://openalex.org/keywords/adjoint-equation","display_name":"Adjoint equation","score":0.5719447731971741},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5666663646697998},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.539240300655365},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4786195158958435},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.47237303853034973},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.44807177782058716},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4267592132091522},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.42302456498146057},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41934558749198914},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.35321033000946045},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.19794344902038574},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18480858206748962},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11440318822860718},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08763647079467773}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8428688049316406},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6989524960517883},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.656733512878418},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.5719447731971741},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5666663646697998},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.539240300655365},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4786195158958435},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.47237303853034973},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.44807177782058716},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4267592132091522},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.42302456498146057},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41934558749198914},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.35321033000946045},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.19794344902038574},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18480858206748962},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11440318822860718},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08763647079467773},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090758179","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090758179","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:CiteSeerX.psu:10.1.1.370.4380","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.370.4380","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/38/26/57/PDF/shapederivative6.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W221766601","https://openalex.org/W560409768","https://openalex.org/W1981515050","https://openalex.org/W1989070662","https://openalex.org/W1992192269","https://openalex.org/W2002873478","https://openalex.org/W2024260176","https://openalex.org/W2041341487","https://openalex.org/W2049524512","https://openalex.org/W2057561640","https://openalex.org/W2082230023","https://openalex.org/W2093432185","https://openalex.org/W2103558875"],"related_works":["https://openalex.org/W938435153","https://openalex.org/W90718935","https://openalex.org/W2680897397","https://openalex.org/W4280607740","https://openalex.org/W1965784592","https://openalex.org/W4229447705","https://openalex.org/W2114432561","https://openalex.org/W2082834779","https://openalex.org/W2056856723","https://openalex.org/W1965080906"],"abstract_inverted_index":{"In":[0],"this":[1,120],"paper,":[2],"compressible,":[3],"stationary":[4],"Navier\u2013Stokes":[5,33,129,164],"equations":[6,130,165,204,209],"are":[7,51,61,131,210],"considered.":[8],"The":[9,26,48,72,97,122,149,158,185],"model":[10],"is":[11,30,104,117,143,156,232,238],"well-posed,":[12],"and":[13,57,112,205,231],"there":[14],"exist":[15],"weak":[16,147],"solutions":[17,50,66,80,126,142,161,201],"in":[18,37,106,145,212,242,251],"bounded":[19],"domains,":[20],"subject":[21],"to":[22,67,83,119,127,162,168,172,202,228],"inhomogeneous":[23],"boundary":[24,34,186,193],"conditions.":[25],"shape":[27,91,98,123,138,153,187,198,224,249],"sensitivity":[28,154,225],"analysis":[29,155,226],"performed":[31],"for":[32,110,178,196,234],"value":[35,194],"problems":[36,195],"the":[38,44,54,58,64,68,78,84,90,94,101,128,137,141,163,169,173,192,197,206,213,243],"framework":[39],"of":[40,43,74,77,86,93,100,125,140,152,160,182,200,215,218,223,245,248],"small":[41,59,75],"perturbations":[42,60,76],"so-called":[45],"approximate":[46,49,79],"solutions.":[47],"determined":[52],"from":[53],"Stokes":[55],"problem,":[56],"given":[62,132],"by":[63,133],"unique":[65],"full":[69],"nonlinear":[70,235],"model.":[71],"differentiability":[73,92,139,159],"with":[81,166],"respect":[82,167],"coefficients":[85],"differential":[87],"operators":[88],"implies":[89],"drag":[95,102],"functional.":[96],"gradient":[99,188],"functional":[103],"derived":[105],"a":[107,146,179],"form":[108,214],"convenient":[109],"computations,":[111],"an":[113,239],"appropriate":[114,233],"adjoint":[115,207],"state":[116,203,208],"introduced":[118],"end.":[121],"derivatives":[124,199],"smooth":[134],"functions;":[135],"however,":[136],"shown":[144],"norm.":[148],"proposed":[150],"method":[151,222],"general.":[157],"data":[170],"leads":[171],"first":[174],"order":[175],"necessary":[176],"conditions":[177],"broad":[180],"class":[181],"optimization":[183,250],"problems.":[184,236],"as":[189,191],"well":[190],"obtained":[211],"singular":[216],"limits":[217],"volume":[219],"integrals.":[220],"This":[221],"seems":[227],"be":[229],"new":[230],"It":[237],"important":[240],"contribution":[241],"field":[244],"numerical":[246],"methods":[247],"fluid":[252],"mechanics.":[253]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}