{"id":"https://openalex.org/W3044685583","doi":"https://doi.org/10.1137/19m1281009","title":"Nonuniqueness of Weak Solutions to the 3 Dimensional Quasi-Geostrophic Equations","display_name":"Nonuniqueness of Weak Solutions to the 3 Dimensional Quasi-Geostrophic Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3044685583","doi":"https://doi.org/10.1137/19m1281009","mag":"3044685583"},"language":"en","primary_location":{"id":"doi:10.1137/19m1281009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1281009","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/A5053645058","display_name":"Matthew Novack","orcid":"https://orcid.org/0000-0002-0477-747X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Matthew Novack","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053645058"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0815,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.94874438,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"52","issue":"4","first_page":"3301","last_page":"3349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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":0.9994000196456909,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.978600025177002,"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":0.9559999704360962,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8265041708946228},{"id":"https://openalex.org/keywords/preprint","display_name":"Preprint","score":0.8113160133361816},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5489296913146973},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.48443368077278137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46198970079421997},{"id":"https://openalex.org/keywords/euler-characteristic","display_name":"Euler characteristic","score":0.44203779101371765},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4154840111732483},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3371093273162842},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19910112023353577},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10272979736328125},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0705595314502716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8265041708946228},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.8113160133361816},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5489296913146973},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.48443368077278137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46198970079421997},{"id":"https://openalex.org/C196433757","wikidata":"https://www.wikidata.org/wiki/Q852973","display_name":"Euler characteristic","level":2,"score":0.44203779101371765},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4154840111732483},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3371093273162842},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19910112023353577},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10272979736328125},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0705595314502716}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1281009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1281009","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":[{"display_name":"Affordable and clean energy","score":0.800000011920929,"id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1503477931","https://openalex.org/W1574784263","https://openalex.org/W1964270654","https://openalex.org/W1980520313","https://openalex.org/W2002399926","https://openalex.org/W2006455026","https://openalex.org/W2007116632","https://openalex.org/W2018766993","https://openalex.org/W2020628192","https://openalex.org/W2023810844","https://openalex.org/W2024249904","https://openalex.org/W2034536348","https://openalex.org/W2047053964","https://openalex.org/W2054352158","https://openalex.org/W2063601135","https://openalex.org/W2069354488","https://openalex.org/W2079654161","https://openalex.org/W2081216912","https://openalex.org/W2085925053","https://openalex.org/W2102375137","https://openalex.org/W2129822331","https://openalex.org/W2155739140","https://openalex.org/W2285817517","https://openalex.org/W2332806608","https://openalex.org/W2464615737","https://openalex.org/W2533734657","https://openalex.org/W2581454467","https://openalex.org/W2593798028","https://openalex.org/W2605513549","https://openalex.org/W2748930849","https://openalex.org/W2806616310","https://openalex.org/W2883158871","https://openalex.org/W2942639054","https://openalex.org/W2953658630","https://openalex.org/W2962727857","https://openalex.org/W2962849048","https://openalex.org/W2962998285","https://openalex.org/W2963192747","https://openalex.org/W2963246686","https://openalex.org/W2963688169","https://openalex.org/W2963700524","https://openalex.org/W2963784458","https://openalex.org/W2963851263","https://openalex.org/W3009452256","https://openalex.org/W3029710649","https://openalex.org/W3098105989","https://openalex.org/W3098208188","https://openalex.org/W3101001753","https://openalex.org/W3102352233","https://openalex.org/W3105292633"],"related_works":["https://openalex.org/W4229365511","https://openalex.org/W3131332557","https://openalex.org/W4211247774","https://openalex.org/W3045462960","https://openalex.org/W4286761081","https://openalex.org/W100995625","https://openalex.org/W4210578026","https://openalex.org/W1938807311","https://openalex.org/W4251903548","https://openalex.org/W3123882228"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,63],"weak":[3],"solutions":[4],"to":[5],"the":[6,12,41,45,53,71,76,100],"3":[7],"dimensional":[8,55],"quasi-geostrophic":[9,46],"system":[10],"in":[11,37],"class":[13],"$C^\\zeta_{t,x}$":[14],"for":[15,75],"$\\zeta<\\frac{1}{5}$":[16],"are":[17],"not":[18],"unique":[19],"and":[20,85,90,117],"may":[21],"achieve":[22],"any":[23],"smooth,":[24],"nonnegative":[25],"energy":[26],"profile.":[27],"Our":[28],"proof":[29],"follows":[30],"a":[31,38,50,92],"convex":[32,72],"integration":[33,73],"scheme":[34,74],"which":[35,94],"utilizes":[36],"crucial":[39],"way":[40],"stratified":[42],"nature":[43],"of":[44,102,107],"velocity":[47],"field,":[48],"providing":[49],"link":[51],"with":[52,70],"2":[54],"(2D)":[56],"Euler":[57,78],"equations.":[58],"In":[59],"fact":[60],"we":[61],"observe":[62],"under":[64],"particular":[65],"circumstances":[66],"our":[67],"construction":[68],"coincides":[69],"2D":[77],"equations":[79],"introduced":[80],"by":[81],"Choffrut,":[82],"De":[83],"Lellis,":[84],"Szek\u00e9lyhidi":[86],"[preprint,":[87],"arxiv.org/abs/1205.1226,":[88],"2012]":[89],"recovers":[91],"result":[93],"can":[95],"already":[96],"be":[97],"inferred":[98],"from":[99],"arguments":[101],"Buckmaster":[103],"et":[104],"al.":[105],"[Ann.":[106],"Math.":[108],"(2),":[109],"182":[110],"(2015),":[111],"pp.":[112,125],"127--172],":[113],"or":[114],"Buckmaster,":[115],"Shkoller,":[116],"Vicol":[118],"[Comm.":[119],"Pure":[120],"Appl.":[121],"Math.,":[122],"12":[123],"(2019),":[124],"1809--1874].":[126]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
