{"id":"https://openalex.org/W2077237510","doi":"https://doi.org/10.1137/120882184","title":"Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations","display_name":"Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2077237510","doi":"https://doi.org/10.1137/120882184","mag":"2077237510"},"language":"en","primary_location":{"id":"doi:10.1137/120882184","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120882184","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/A5079798275","display_name":"Andrea R. Nahmod","orcid":"https://orcid.org/0000-0002-3195-7249"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrea R. Nahmod","raw_affiliation_strings":["University of Massachusetts"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102006068","display_name":"Nata\u0161a Pavlovi\u0107","orcid":"https://orcid.org/0000-0001-6665-1963"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nata\u0161a Pavlovi\u0107","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5009081428","display_name":"Gigliola Staffilani","orcid":"https://orcid.org/0000-0003-1382-9435"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gigliola Staffilani","raw_affiliation_strings":["Massachusetts Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5079798275"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.4208,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.98771536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"45","issue":"6","first_page":"3431","last_page":"3452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9990000128746033,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/supercritical-fluid","display_name":"Supercritical fluid","score":0.8845850229263306},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.818545937538147},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5092765092849731},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.42756152153015137},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4255436956882477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1273033618927002},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.07294774055480957},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.07117876410484314},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05679914355278015}],"concepts":[{"id":"https://openalex.org/C118419359","wikidata":"https://www.wikidata.org/wiki/Q682585","display_name":"Supercritical fluid","level":2,"score":0.8845850229263306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.818545937538147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5092765092849731},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.42756152153015137},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4255436956882477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1273033618927002},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.07294774055480957},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.07117876410484314},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05679914355278015},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120882184","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120882184","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":[{"id":"https://metadata.un.org/sdg/7","score":0.7599999904632568,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2531442273","display_name":"From many body quantum dynamics to nonlinear dispersive PDEs, and back","funder_award_id":"1101192","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6492772265","display_name":"New perspectives on dispersive equations","funder_award_id":"1068815","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W825873024","https://openalex.org/W1968102647","https://openalex.org/W1980560954","https://openalex.org/W1982418511","https://openalex.org/W1984052922","https://openalex.org/W2021073558","https://openalex.org/W2021964921","https://openalex.org/W2033305412","https://openalex.org/W2035762669","https://openalex.org/W2037403153","https://openalex.org/W2043876702","https://openalex.org/W2049133293","https://openalex.org/W2052982407","https://openalex.org/W2081654599","https://openalex.org/W2089008029","https://openalex.org/W2091176842","https://openalex.org/W2099224503","https://openalex.org/W2128028283","https://openalex.org/W2319542184","https://openalex.org/W2394107644","https://openalex.org/W2467278134","https://openalex.org/W2596083410","https://openalex.org/W2623423078","https://openalex.org/W2964128815","https://openalex.org/W3099862992","https://openalex.org/W3101213000","https://openalex.org/W3102383043","https://openalex.org/W4246454803"],"related_works":["https://openalex.org/W3196163622","https://openalex.org/W2370685986","https://openalex.org/W4388805554","https://openalex.org/W2371292460","https://openalex.org/W2040168466","https://openalex.org/W2130313128","https://openalex.org/W7632529","https://openalex.org/W2382967792","https://openalex.org/W2316032560","https://openalex.org/W4244441149"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,43],"show":[4,55],"that":[5,56],"after":[6],"suitable":[7],"data":[8,48],"randomization":[9],"there":[10],"exists":[11],"a":[12,41],"large":[13,47],"set":[14],"of":[15],"supercritical":[16,49],"periodic":[17],"initial":[18],"data,":[19],"in":[20,57],"$H^{-\\alpha}(\\boldsymbol{T}^d)$":[21],"for":[22,27,34],"some":[23],"$\\alpha(d)":[24],">":[25],"0$,":[26],"both":[28],"two-":[29],"and":[30],"three-dimensional":[31],"Navier--Stokes":[32],"equations":[33],"which":[35],"global":[36,50,61],"energy":[37],"bounds":[38],"hold.":[39],"As":[40],"consequence,":[42],"obtain":[44],"almost":[45],"sure":[46],"weak":[51,62],"solutions.":[52],"We":[53],"also":[54],"two":[58],"dimensions":[59],"these":[60],"solutions":[63],"are":[64],"unique.":[65]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}