{"id":"https://openalex.org/W2343214441","doi":"https://doi.org/10.1137/16m1073881","title":"A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing","display_name":"A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2343214441","doi":"https://doi.org/10.1137/16m1073881","mag":"2343214441"},"language":"en","primary_location":{"id":"doi:10.1137/16m1073881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1073881","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1604.08396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017651148","display_name":"Miroslav Bul\u00ed\u010dek","orcid":"https://orcid.org/0000-0003-2380-3458"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]}],"countries":["CZ","PL"],"is_corresponding":true,"raw_author_name":"M. Bul\u00cd\u010dek","raw_affiliation_strings":["Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055861081","display_name":"Jan Burczak","orcid":"https://orcid.org/0000-0002-6963-5448"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]}],"countries":["CZ","PL"],"is_corresponding":false,"raw_author_name":"J. Burczak","raw_affiliation_strings":["Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072376364","display_name":"Sebastian Schwarzacher","orcid":"https://orcid.org/0000-0003-2415-1172"},"institutions":[{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ","PL"],"is_corresponding":false,"raw_author_name":"S. Schwarzacher","raw_affiliation_strings":["Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles Uni-versity in Prague, Sokolovsk\u00e1 83, 186 75 Prague, Czech Republic","institution_ids":["https://openalex.org/I21250087"]},{"raw_affiliation_string":"Institute of Mathematics , Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656 Warsaw, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017651148"],"corresponding_institution_ids":["https://openalex.org/I21250087","https://openalex.org/I4210137370","https://openalex.org/I99542240"],"apc_list":null,"apc_paid":null,"fwci":3.2224,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.9073702,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"48","issue":"6","first_page":"4241","last_page":"4267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9950000047683716,"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":0.9950000047683716,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9950000047683716,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9943000078201294,"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":0.8696019649505615},{"id":"https://openalex.org/keywords/solenoidal-vector-field","display_name":"Solenoidal vector field","score":0.8445427417755127},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7639652490615845},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.696094274520874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5841935873031616},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5224375128746033},{"id":"https://openalex.org/keywords/non-newtonian-fluid","display_name":"Non-Newtonian fluid","score":0.505760669708252},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.4620043933391571},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.42885300517082214},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.4242521822452545},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.2498166859149933},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.15510037541389465}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8696019649505615},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.8445427417755127},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7639652490615845},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.696094274520874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5841935873031616},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5224375128746033},{"id":"https://openalex.org/C84403224","wikidata":"https://www.wikidata.org/wiki/Q860589","display_name":"Non-Newtonian fluid","level":2,"score":0.505760669708252},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.4620043933391571},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.42885300517082214},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.4242521822452545},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2498166859149933},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.15510037541389465},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1073881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1073881","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:arXiv.org:1604.08396","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.08396","pdf_url":"https://arxiv.org/pdf/1604.08396","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1604.08396","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.08396","pdf_url":"https://arxiv.org/pdf/1604.08396","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7476073704","display_name":null,"funder_award_id":"PRVOUK P47","funder_id":"https://openalex.org/F4320309755","funder_display_name":"Univerzita Karlova v Praze"}],"funders":[{"id":"https://openalex.org/F4320309755","display_name":"Univerzita Karlova v Praze","ror":"https://ror.org/024d6js02"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W106962200","https://openalex.org/W144938099","https://openalex.org/W202544164","https://openalex.org/W651321014","https://openalex.org/W1485957485","https://openalex.org/W1525219438","https://openalex.org/W1547458735","https://openalex.org/W1573702861","https://openalex.org/W1584610719","https://openalex.org/W1654491902","https://openalex.org/W1967421336","https://openalex.org/W1967470443","https://openalex.org/W1970049507","https://openalex.org/W1987123778","https://openalex.org/W2009706884","https://openalex.org/W2013152925","https://openalex.org/W2035814641","https://openalex.org/W2053188289","https://openalex.org/W2067319710","https://openalex.org/W2068228997","https://openalex.org/W2076249177","https://openalex.org/W2079239245","https://openalex.org/W2083230936","https://openalex.org/W2083819240","https://openalex.org/W2096541610","https://openalex.org/W2112166131","https://openalex.org/W2118701320","https://openalex.org/W2146785120","https://openalex.org/W2149461673","https://openalex.org/W2150879147","https://openalex.org/W2244849413","https://openalex.org/W2256001351","https://openalex.org/W2257419191","https://openalex.org/W2335551976","https://openalex.org/W3099149002","https://openalex.org/W3100249302","https://openalex.org/W3100519063","https://openalex.org/W3104155247","https://openalex.org/W4231993343","https://openalex.org/W4249667782","https://openalex.org/W4250074289"],"related_works":["https://openalex.org/W2025438663","https://openalex.org/W2018229445","https://openalex.org/W4297752088","https://openalex.org/W2996354014","https://openalex.org/W3193153203","https://openalex.org/W223118542","https://openalex.org/W1979120450","https://openalex.org/W2170335641","https://openalex.org/W3024323046","https://openalex.org/W2963349950"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,68,100],"model":[3],"of":[4,41,77,102],"steady,":[5],"incompressible":[6,117],"non-Newtonian":[7],"flow":[8],"with":[9,45,55,65,84],"neglected":[10],"convective":[11],"term":[12],"under":[13],"external":[14],"forcing.":[15],"Our":[16],"structural":[17],"assumptions":[18],"allow":[19],"for":[20,82,124,130],"certain":[21],"nondegenerate":[22],"power-law":[23],"or":[24],"Carreau-type":[25],"fluids.":[26,118],"Within":[27],"our":[28,125],"setting,":[29],"we":[30],"provide":[31],"the":[32,61,89,135,142],"full-range":[33],"theory,":[34],"namely,":[35,60],"existence,":[36],"optimal":[37],"regularity,":[38],"and":[39,79,107,141],"uniqueness":[40,80],"solutions,":[42],"not":[43],"only":[44],"respect":[46,56],"to":[47,50,57,116],"forcing":[48,83],"belonging":[49],"Lebesgue":[51,63],"spaces,":[52,64],"but":[53],"also":[54],"their":[58],"refinements,":[59],"weighted":[62,96],"weights":[66],"in":[67,95],"respective":[69],"Muckenhoupt":[70],"class.":[71],"The":[72],"analytical":[73],"highlight":[74],"is":[75,99],"derivation":[76],"existence":[78],"theory":[81],"its":[85],"regularity":[86],"well":[87],"below":[88],"natural":[90],"duality":[91],"exponent,":[92],"via":[93],"estimates":[94],"spaces.":[97],"It":[98],"generalization":[101],"[M.":[103],"Bul\u00ed\u010dek,":[104],"L.":[105],"Diening,":[106],"S.":[108],"Schwarzacher,":[109],"Anal.":[110],"PDE,":[111],"9":[112],"(2016),":[113],"pp.":[114],"1115--1151]":[115],"Moreover,":[119],"two":[120],"technical":[121],"results,":[122],"needed":[123],"analysis,":[126],"may":[127],"be":[128],"useful":[129],"further":[131],"studies.":[132],"They":[133],"are":[134],"solenoidal,":[136],"weighted,":[137],"biting":[138],"div-curl":[139],"lemma":[140],"solenoidal":[143],"Lipschitz":[144],"approximations":[145],"on":[146],"domains.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
