{"id":"https://openalex.org/W4392812112","doi":"https://doi.org/10.1137/23m1563141","title":"Sharp Nonuniqueness of Solutions to Stochastic Navier\u2013Stokes Equations","display_name":"Sharp Nonuniqueness of Solutions to Stochastic Navier\u2013Stokes Equations","publication_year":2024,"publication_date":"2024-03-14","ids":{"openalex":"https://openalex.org/W4392812112","doi":"https://doi.org/10.1137/23m1563141"},"language":"en","primary_location":{"id":"doi:10.1137/23m1563141","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1563141","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/A5002034501","display_name":"Weiquan Chen","orcid":"https://orcid.org/0000-0002-2465-8697"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiquan Chen","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001295341","display_name":"Zhao Dong","orcid":"https://orcid.org/0000-0003-3754-1524"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao Dong","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007237966","display_name":"Xiangchan Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangchan Zhu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.6072,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.98645085,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"2","first_page":"2248","last_page":"2285"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"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":0.9995999932289124,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9918000102043152,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9751999974250793,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.873694896697998},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7682738900184631},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5863088965415955},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5197812914848328},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4710554778575897},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.46578067541122437},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.44045186042785645},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.41265520453453064},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39416226744651794},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1461029350757599},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10117512941360474}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.873694896697998},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7682738900184631},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5863088965415955},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5197812914848328},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4710554778575897},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.46578067541122437},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.44045186042785645},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.41265520453453064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39416226744651794},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1461029350757599},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10117512941360474},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1563141","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1563141","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1428129756","display_name":null,"funder_award_id":"CRC 1283","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3530863183","display_name":null,"funder_award_id":"2020YFA0712700","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G6012806810","display_name":null,"funder_award_id":"2020003","funder_id":"https://openalex.org/F4320335892","funder_display_name":"Youth Innovation Promotion Association"},{"id":"https://openalex.org/G6589251086","display_name":null,"funder_award_id":"12090014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7797169195","display_name":null,"funder_award_id":"2008DP173182","funder_id":"https://openalex.org/F4320335892","funder_display_name":"Youth Innovation Promotion Association"},{"id":"https://openalex.org/G8319019752","display_name":"\u975e\u5c40\u90e8\u72c4\u6c0f\u578b\u548c\u968f\u673a\u504f\u5fae\u5206\u65b9\u7a0b\u82e5\u5e72\u95ee\u9898\u7814\u7a76","funder_award_id":"11931004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8533620077","display_name":null,"funder_award_id":"12288201","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G876735084","display_name":null,"funder_award_id":"2022YFA1006300","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335892","display_name":"Youth Innovation Promotion Association","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W6548635","https://openalex.org/W1980520313","https://openalex.org/W1980560954","https://openalex.org/W1982418511","https://openalex.org/W2007599297","https://openalex.org/W2011844796","https://openalex.org/W2021964921","https://openalex.org/W2023810844","https://openalex.org/W2027690576","https://openalex.org/W2052246295","https://openalex.org/W2055459591","https://openalex.org/W2058440918","https://openalex.org/W2067971241","https://openalex.org/W2077514318","https://openalex.org/W2078140724","https://openalex.org/W2079505476","https://openalex.org/W2099224503","https://openalex.org/W2129822331","https://openalex.org/W2149674112","https://openalex.org/W2153678797","https://openalex.org/W2155739140","https://openalex.org/W2268506128","https://openalex.org/W2318624729","https://openalex.org/W2332806608","https://openalex.org/W2338895534","https://openalex.org/W2607645898","https://openalex.org/W2620284697","https://openalex.org/W2962849048","https://openalex.org/W2962998285","https://openalex.org/W2963012808","https://openalex.org/W2963192747","https://openalex.org/W2963551825","https://openalex.org/W2964063216","https://openalex.org/W2979313970","https://openalex.org/W3009452256","https://openalex.org/W3086487105","https://openalex.org/W3095715602","https://openalex.org/W3100994666","https://openalex.org/W3101001753","https://openalex.org/W3103598992","https://openalex.org/W3134694139","https://openalex.org/W3202856231","https://openalex.org/W3203845654","https://openalex.org/W3209887221","https://openalex.org/W4281570200","https://openalex.org/W4319923081"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W4402427056","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{".In":[0],"this":[1],"paper":[2],"we":[3,25,52,139,151],"establish":[4],"a":[5,86,141],"sharp":[6,59],"nonuniqueness":[7],"result":[8,57],"for":[9,18,44,72,93],"stochastic":[10,87,95,143],"\\(d\\)-dimensional":[11,96],"(\\(d\\geq":[12],"2\\))":[13],"incompressible":[14,97],"Navier\u2013Stokes":[15,169],"equations.":[16],"First,":[17],"every":[19],"divergence-free":[20],"initial":[21],"condition":[22],"in":[23,38,60,67,121],"\\(L^2\\)":[24],"show":[26],"existence":[27,101],"of":[28,70,89,102,145],"infinitly":[29],"many":[30,104],"global-in-time":[31,105],"probabilistically":[32,106],"strong":[33,107,173],"and":[34,108,124,158],"analytically":[35,109],"weak":[36,110],"solutions":[37,111,161],"the":[39,55,61,68,94,100,116,146,163],"class":[40,69],"\\(L^\\alpha":[41],"(\\Omega,L^p_tL^\\infty":[42],")\\)":[43],"any":[45],"\\(1\\leq":[46],"p\\lt":[47],"2,\\alpha":[48],"\\geq":[49],"1\\).":[50],"Second,":[51],"prove":[53],"that":[54,63,80],"above":[56],"is":[58,85,112],"sense":[62],"pathwise":[64],"uniqueness":[65],"holds":[66],"\\(L^p_tL^q\\)":[71],"some":[73],"\\(p\\in":[74],"[2,\\infty":[75],"],q\\in":[76],"(2,\\infty":[77],"]\\)":[78],"such":[79],"\\(\\frac":[81],"2{p}+\\frac{d}{q}\\leq":[82],"1\\),":[83],"which":[84],"version":[88,144],"Ladyzhenskaya\u2013Prodi\u2013Serrin":[90],"criteria.":[91],"Moreover,":[92],"Euler":[98,171],"equation,":[99],"infinitely":[103],"obtained.":[113],"Compared":[114],"to":[115,131],"stopping":[117],"time":[118,165],"argument":[119],"used":[120],"Hoffmanov\u00e1,":[122],"Zhu,":[123],"Zhu":[125],"[J.":[126],"Eur.":[127],"Math.":[128],"Soc.":[129],"(JEMS),":[130],"appear;":[132],"Ann.":[133],"Probab.,":[134],"51":[135],"(2023),":[136],"pp.":[137],"524\u2013579],":[138],"developed":[140],"new":[142],"convex":[147,155],"integration.":[148],"More":[149],"precisely,":[150],"introduce":[152],"expectation":[153],"during":[154],"integration":[156],"scheme":[157],"construct":[159],"directly":[160],"on":[162],"whole":[164],"interval":[166],"\\([0,\\infty":[167],")\\).Keywordsstochastic":[168],"equationsstochastic":[170],"equationsprobabilistically":[172],"solutionssharp":[174],"nonuniquenessconvex":[175],"integrationMSC":[176],"codes60H1535R6035Q30":[177]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}