{"id":"https://openalex.org/W2069097584","doi":"https://doi.org/10.1137/040612336","title":"Navier--Stokes Equations with Navier Boundary Conditions for a Bounded Domain in the Plane","display_name":"Navier--Stokes Equations with Navier Boundary Conditions for a Bounded Domain in the Plane","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2069097584","doi":"https://doi.org/10.1137/040612336","mag":"2069097584"},"language":"en","primary_location":{"id":"doi:10.1137/040612336","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612336","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5078338329","display_name":"James P. Kelliher","orcid":"https://orcid.org/0000-0002-5883-2032"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James P. Kelliher","raw_affiliation_strings":["Department of Mathematics, University of Texas, Austin, Texas, 78712"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas, Austin, Texas, 78712","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078338329"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":3.156,"has_fulltext":false,"cited_by_count":182,"citation_normalized_percentile":{"value":0.91054614,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"38","issue":"1","first_page":"210","last_page":"232"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9916999936103821,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6702905297279358},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.6447196006774902},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6061549186706543},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5997514128684998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5476006269454956},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.5451436042785645},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5445185303688049},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5344229340553284},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5145463347434998},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.47029897570610046},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.4233905076980591},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3565777540206909},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.343616783618927},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.1065526008605957}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6702905297279358},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.6447196006774902},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6061549186706543},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5997514128684998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5476006269454956},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.5451436042785645},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5445185303688049},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5344229340553284},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5145463347434998},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.47029897570610046},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.4233905076980591},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3565777540206909},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.343616783618927},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.1065526008605957},{"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/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040612336","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040612336","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.339.9241","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.339.9241","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/math-ph/0409012v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.541.2521","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.541.2521","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucr.edu/~kelliher/papers/SIMA2006.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.85.5361","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.85.5361","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.brown.edu/~kelliher/papers/SIMA2006.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":29,"referenced_works":["https://openalex.org/W74811803","https://openalex.org/W590529998","https://openalex.org/W617437241","https://openalex.org/W1496674715","https://openalex.org/W1573547614","https://openalex.org/W1586623601","https://openalex.org/W1598074861","https://openalex.org/W1667151533","https://openalex.org/W1866311589","https://openalex.org/W1969598505","https://openalex.org/W1973576205","https://openalex.org/W2002187956","https://openalex.org/W2011208969","https://openalex.org/W2026803537","https://openalex.org/W2071273793","https://openalex.org/W2073149189","https://openalex.org/W2076582418","https://openalex.org/W2079131035","https://openalex.org/W2083421003","https://openalex.org/W2090160848","https://openalex.org/W2116961686","https://openalex.org/W2132834302","https://openalex.org/W2145789337","https://openalex.org/W2225972081","https://openalex.org/W2477040106","https://openalex.org/W3091814460","https://openalex.org/W4247885862","https://openalex.org/W4249764880","https://openalex.org/W4292360407"],"related_works":["https://openalex.org/W2153510147","https://openalex.org/W4385681600","https://openalex.org/W2165279409","https://openalex.org/W2563697776","https://openalex.org/W1643467562","https://openalex.org/W3134117708","https://openalex.org/W2029030586","https://openalex.org/W2964194582","https://openalex.org/W2953844359","https://openalex.org/W1995739312"],"abstract_inverted_index":{"We":[0,93,190],"consider":[1],"solutions":[2,169,199],"to":[3,122,170,178,181,200,220,223],"the":[4,29,52,55,79,95,104,134,137,140,162,171,179,182,186,198,201,221,224,228,241],"Navier--Stokes":[5,172,202,225],"equations":[6,173,184,203,226],"with":[7,18,143,174,204,227],"Navier":[8,22,175,205],"boundary":[9,23,74,176,206,231],"conditions":[10,24,75,177,207,232],"in":[11,16,28,71,78,166,185,210,212,216,218],"a":[12,19,58,64,130,158],"bounded":[13],"domain":[14],"$\\Omega$":[15],"${\\ensuremath{\\BB{R}}}^2$":[17],"$C^2$-boundary":[20],"$\\Gamma$.":[21],"can":[25],"be":[26],"expressed":[27],"form":[30],"$\\omega(v)":[31],"=":[32,45,84],"(2":[33],"\\kappa":[34],"-":[35],"{\\ensuremath{\\alpha}})":[36],"v":[37,50],"\\cdot":[38,43],"{\\mbox{\\boldmath":[39],"$\\tau$}}$":[40,63],"and":[41,68,90,98,109,111,117,126,147,154,214],"$v":[42],"\\mathbf{n}":[44],"0$":[46],"on":[47,133,152,161,240],"$\\Gamma$,":[48],"where":[49,82],"is":[51,70],"velocity,":[53],"$\\omega(v)$":[54],"vorticity,":[56],"$\\mathbf{n}$":[57],"unit":[59,65],"normal":[60],"vector,":[61,67],"${\\mbox{\\boldmath":[62],"tangent":[66],"${\\ensuremath{\\alpha}}$":[69,236],"$L^{\\ensuremath{\\infty}}(\\Gamma)$.":[72],"These":[73],"were":[76],"studied":[77],"special":[80],"case":[81],"${\\ensuremath{\\alpha}}":[83],"2":[85],"\\kappa$":[86],"by":[87],"J.-L.":[88],"Lions":[89],"P.-L.":[91],"Lions.":[92],"establish":[94],"existence,":[96],"uniqueness,":[97],"regularity":[99],"of":[100,106,112,136,139,164,168],"such":[101],"solutions,":[102],"extending":[103],"work":[105],"Clopeau,":[107],"Mikeli{ć,":[108],"Robert":[110],"Lopes":[113],"Filho,":[114],"Nussenzveig":[115],"Lopes,":[116],"Planas,":[118],"which":[119],"was":[120],"restricted":[121],"simply":[123],"connected":[124],"domains":[125],"nonnegative":[127],"${\\ensuremath{\\alpha}}$.":[128],"Assuming":[129],"particular":[131],"bound":[132,160],"growth":[135],"$L^p$-norms":[138],"initial":[141,196],"vorticity":[142],"p":[144],"(\\textit{Yudovich":[145],"vorticity}),":[146],"also":[148,191],"assuming":[149],"additional":[150],"smoothness":[151],"$\\Gamma$":[153],"${\\ensuremath{\\alpha}}$,":[155],"we":[156,234],"obtain":[157],"uniform-in-time":[159],"rate":[163],"convergence":[165],"$L^2(\\Omega)$":[167],"solution":[180,222],"Euler":[183],"vanishing":[187],"viscosity":[188],"limit.":[189],"show":[192],"that":[193],"for":[194],"smoother":[195],"velocities,":[197],"converge":[208],"uniformly":[209,239],"time":[211,217],"$L^2(\\Omega)$,":[213],"$L^2$":[215],"$\\dot{H}^1(\\Omega)$,":[219],"usual":[229],"no-slip":[230],"as":[233],"let":[235],"grow":[237],"large":[238],"boundary.":[242]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":19}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}