{"id":"https://openalex.org/W2026257474","doi":"https://doi.org/10.1137/100814639","title":"Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows","display_name":"Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2026257474","doi":"https://doi.org/10.1137/100814639","mag":"2026257474"},"language":"en","primary_location":{"id":"doi:10.1137/100814639","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814639","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/A5020285342","display_name":"Xiangdi Huang","orcid":"https://orcid.org/0000-0003-1415-6455"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangdi Huang","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100337069","display_name":"Jing Li","orcid":"https://orcid.org/0000-0003-1620-5126"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101898018","display_name":"Zhouping Xin","orcid":"https://orcid.org/0000-0002-7434-2404"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhouping Xin","raw_affiliation_strings":["The Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.8982,"has_fulltext":false,"cited_by_count":184,"citation_normalized_percentile":{"value":0.99677917,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"43","issue":"4","first_page":"1872","last_page":"1886"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9998000264167786,"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":0.9998000264167786,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9887999892234802,"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":0.7693588733673096},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.7221136689186096},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7178889513015747},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6423454880714417},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5298507213592529},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5057005882263184},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14597102999687195},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12545138597488403}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7693588733673096},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.7221136689186096},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7178889513015747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6423454880714417},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5298507213592529},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5057005882263184},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14597102999687195},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12545138597488403},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100814639","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814639","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:10.1.1.762.665","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.665","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/1004.4748.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":32,"referenced_works":["https://openalex.org/W59832175","https://openalex.org/W134493960","https://openalex.org/W1481464202","https://openalex.org/W1496904369","https://openalex.org/W1569509154","https://openalex.org/W1573547614","https://openalex.org/W1868633469","https://openalex.org/W1969543804","https://openalex.org/W1971154593","https://openalex.org/W1981659965","https://openalex.org/W1996952201","https://openalex.org/W2000936983","https://openalex.org/W2008616327","https://openalex.org/W2009353889","https://openalex.org/W2012955336","https://openalex.org/W2013547690","https://openalex.org/W2023699807","https://openalex.org/W2025611614","https://openalex.org/W2028052783","https://openalex.org/W2033981626","https://openalex.org/W2044532587","https://openalex.org/W2051748402","https://openalex.org/W2069980492","https://openalex.org/W2072539439","https://openalex.org/W2087837589","https://openalex.org/W2151847866","https://openalex.org/W2168162898","https://openalex.org/W2369386221","https://openalex.org/W2470769821","https://openalex.org/W2964118263","https://openalex.org/W3098959926","https://openalex.org/W4253117495"],"related_works":["https://openalex.org/W2012983134","https://openalex.org/W4388599312","https://openalex.org/W2053355289","https://openalex.org/W2368811332","https://openalex.org/W4205276374","https://openalex.org/W2090218458","https://openalex.org/W3208095355","https://openalex.org/W2390251251","https://openalex.org/W1972617237","https://openalex.org/W2177370417"],"abstract_inverted_index":{"We":[0],"extend":[1],"the":[2,8,15,25,29,35,38,46,49,54,57,60,63,66,72,76,88,92],"well-known":[3],"Serrin's":[4,50,89],"blowup":[5],"criterion":[6],"for":[7,24],"three-dimensional":[9],"(3D)":[10],"incompressible":[11],"Navier\u2013Stokes":[12,32],"equations":[13,33],"to":[14],"3D":[16,30],"viscous":[17],"compressible":[18,31],"cases.":[19],"It":[20],"is":[21,68,80,85],"shown":[22],"that":[23,74],"Cauchy":[26],"problem":[27],"of":[28,56,62,65],"in":[34,71,97],"whole":[36],"space,":[37],"strong":[39],"or":[40,59,83],"smooth":[41],"solution":[42],"exists":[43],"globally":[44],"if":[45],"velocity":[47,67,93],"satisfies":[48],"condition":[51,90],"and":[52],"either":[53,75],"supernorm":[55],"density":[58],"$L^1(0,T;L^\\infty)$-norm":[61],"divergence":[64],"bounded.":[69],"Furthermore,":[70],"case":[73],"shear":[77],"viscosity":[78],"coefficient":[79],"suitably":[81],"large":[82],"there":[84],"no":[86],"vacuum,":[87],"on":[91],"can":[94],"be":[95],"removed":[96],"this":[98],"criterion.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":17},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":13}],"updated_date":"2026-08-12T07:12:00.856984","created_date":"2025-10-10T00:00:00"}