{"id":"https://openalex.org/W2913963899","doi":"https://doi.org/10.1137/19m1244895","title":"On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion","display_name":"On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2913963899","doi":"https://doi.org/10.1137/19m1244895","mag":"2913963899"},"language":"en","primary_location":{"id":"doi:10.1137/19m1244895","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1244895","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/1902.04853","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jan Blechta","orcid":"https://orcid.org/0000-0001-8978-4187"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jan Blechta","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Josef M\u00e1lek","orcid":"https://orcid.org/0000-0001-6920-0842"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josef M\u00e1lek","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"K. R. Rajagopal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. R. Rajagopal","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6993,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.89925194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"52","issue":"2","first_page":"1232","last_page":"1289"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.4262999892234802,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T11366","display_name":"Elasticity and Material Modeling","score":0.4262999892234802,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10940","display_name":"Navier-Stokes equation solutions","score":0.249099999666214,"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/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.09570000320672989,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/compressibility","display_name":"Compressibility","score":0.6204000115394592},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5320000052452087},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.48899999260902405},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.48420000076293945},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.47279998660087585},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.4255000054836273},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.41909998655319214},{"id":"https://openalex.org/keywords/slip","display_name":"Slip (aerodynamics)","score":0.4129999876022339},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.38440001010894775}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6814000010490417},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6204000115394592},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5320000052452087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5235000252723694},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.4255000054836273},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C195268267","wikidata":"https://www.wikidata.org/wiki/Q1928883","display_name":"Slip (aerodynamics)","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C16304620","wikidata":"https://www.wikidata.org/wiki/Q1396948","display_name":"No-slip condition","level":4,"score":0.37299999594688416},{"id":"https://openalex.org/C43133876","wikidata":"https://www.wikidata.org/wiki/Q172145","display_name":"Fluid mechanics","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.3515999913215637},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34619998931884766},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.3199999928474426},{"id":"https://openalex.org/C51336717","wikidata":"https://www.wikidata.org/wiki/Q5532445","display_name":"Generalized Newtonian fluid","level":4,"score":0.31189998984336853},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C191236761","wikidata":"https://www.wikidata.org/wiki/Q10862968","display_name":"Herschel\u2013Bulkley fluid","level":3,"score":0.2955000102519989},{"id":"https://openalex.org/C2781217745","wikidata":"https://www.wikidata.org/wiki/Q1053779","display_name":"Euler system","level":3,"score":0.2953000068664551},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C71351571","wikidata":"https://www.wikidata.org/wiki/Q7935890","display_name":"Viscous liquid","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C2984161354","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid motion","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.27720001339912415},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2644999921321869}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1244895","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1244895","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:1902.04853","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.04853","pdf_url":"https://arxiv.org/pdf/1902.04853","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:1902.04853","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.04853","pdf_url":"https://arxiv.org/pdf/1902.04853","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/G1840641927","display_name":null,"funder_award_id":"GA CR 18-12719S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G753968184","display_name":null,"funder_award_id":"18-12719S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W99114895","https://openalex.org/W112686973","https://openalex.org/W1870863896","https://openalex.org/W1966290891","https://openalex.org/W1967107812","https://openalex.org/W1967470443","https://openalex.org/W1975407520","https://openalex.org/W1978764927","https://openalex.org/W1980520313","https://openalex.org/W1983154719","https://openalex.org/W1998046278","https://openalex.org/W2006471411","https://openalex.org/W2007727618","https://openalex.org/W2020871562","https://openalex.org/W2026225021","https://openalex.org/W2033762420","https://openalex.org/W2035885341","https://openalex.org/W2036180733","https://openalex.org/W2036239259","https://openalex.org/W2038405999","https://openalex.org/W2039052667","https://openalex.org/W2041268266","https://openalex.org/W2044975742","https://openalex.org/W2048525720","https://openalex.org/W2056492307","https://openalex.org/W2056712709","https://openalex.org/W2057554392","https://openalex.org/W2059188813","https://openalex.org/W2062002217","https://openalex.org/W2062974973","https://openalex.org/W2064995425","https://openalex.org/W2073370369","https://openalex.org/W2080162144","https://openalex.org/W2083230936","https://openalex.org/W2084768159","https://openalex.org/W2087646300","https://openalex.org/W2091516904","https://openalex.org/W2112166131","https://openalex.org/W2117564652","https://openalex.org/W2146785120","https://openalex.org/W2249942971","https://openalex.org/W2328799684","https://openalex.org/W2464735920","https://openalex.org/W2485114271","https://openalex.org/W2793387677","https://openalex.org/W2892290260","https://openalex.org/W2919924423","https://openalex.org/W2962893622","https://openalex.org/W2963357469","https://openalex.org/W2963888846","https://openalex.org/W2963952534","https://openalex.org/W2964324267","https://openalex.org/W3099272999"],"related_works":[],"abstract_inverted_index":{"In":[0,98],"the":[1,5,22,26,51,92,96,99,103,120],"first":[2],"part":[3,101],"of":[4,12,102,119,141],"paper":[6],"we":[7,54,105],"provide":[8],"a":[9,17,73,83,107],"new":[10],"classification":[11,84],"incompressible":[13],"fluids":[14,39,52,61,114,143],"characterized":[15],"by":[16],"continuous":[18],"monotone":[19],"relation":[20],"between":[21],"velocity":[23],"gradient":[24],"and":[25,46,70,128,138],"Cauchy":[27],"stress.":[28],"The":[29],"considered":[30],"class":[31],"includes":[32],"Euler":[33,66,113],"fluids,":[34,36,45,59],"Navier--Stokes":[35],"classical":[37],"power-law":[38,44],"as":[40,42,57,64,72,91,132,134],"well":[41,133],"stress":[43],"their":[47],"various":[48],"generalizations":[49],"including":[50],"that":[53,62,88],"refer":[55],"to":[56,126],"activated":[58,112],"namely,":[60],"behave":[63,71],"an":[65],"fluid":[67,75],"prior":[68],"activation":[69,77],"viscous":[74],"once":[76],"takes":[78],"place.":[79],"We":[80],"also":[81],"present":[82],"concerning":[85],"boundary":[86,121],"conditions":[87,122],"are":[89,147],"viewed":[90],"constitutive":[93],"relations":[94],"on":[95],"boundary.":[97],"second":[100],"paper,":[104],"develop":[106],"robust":[108],"mathematical":[109],"theory":[110],"for":[111],"associated":[115],"with":[116],"different":[117],"types":[118],"ranging":[123],"from":[124],"no-slip":[125],"free-slip":[127],"include":[129],"Navier's":[130],"slip":[131],"stick-slip.":[135],"Both":[136],"steady":[137],"unsteady":[139],"flows":[140],"such":[142],"in":[144],"three-dimensional":[145],"domains":[146],"analyzed.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":3}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2019-02-21T00:00:00"}
