{"id":"https://openalex.org/W4378942455","doi":"https://doi.org/10.4007/annals.2026.204.1.4","title":"The $L^3$-based strong Onsager theorem","display_name":"The $L^3$-based strong Onsager theorem","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W4378942455","doi":"https://doi.org/10.4007/annals.2026.204.1.4"},"language":"en","primary_location":{"id":"doi:10.4007/annals.2026.204.1.4","doi":"https://doi.org/10.4007/annals.2026.204.1.4","is_oa":false,"landing_page_url":"https://doi.org/10.4007/annals.2026.204.1.4","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2305.18509","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039051726","display_name":"Vikram Giri","orcid":"https://orcid.org/0000-0002-3047-9927","observed_orcids":["https://orcid.org/0000-0002-3047-9927"]},"institutions":[{"id":"https://openalex.org/I202697423","display_name":"University of Zurich","ror":"https://ror.org/02crff812","country_code":"CH","type":"education","lineage":["https://openalex.org/I202697423"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Vikram Giri","raw_affiliation_strings":["Institute of Mathematics, University of Z\u00fcrich,  Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-3047-9927","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Z\u00fcrich,  Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I202697423"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101303268","display_name":"HyunjuVE Kwon","orcid":"https://orcid.org/0000-0003-4093-3991","observed_orcids":["https://orcid.org/0000-0003-4093-3991"]},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Hyunju Kwon","raw_affiliation_strings":["Department of Mathematics, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-4093-3991","affiliations":[{"raw_affiliation_string":"Department of Mathematics, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053645058","display_name":"Matthew Novack","orcid":"https://orcid.org/0000-0002-0477-747X","observed_orcids":["https://orcid.org/0000-0002-0477-747X"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Novack","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN,  USA"],"raw_orcid":"https://orcid.org/0000-0002-0477-747X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN,  USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":36.9663,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.99932137,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"204","issue":"1","first_page":"265","last_page":"421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9984999895095825,"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":0.9984999895095825,"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":0.00019999999494757503,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00019999999494757503,"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/3d-euler-equations","display_name":"three-dimensional Euler equations","score":0.8870000243186951},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.9110000133514404},{"id":"https://openalex.org/keywords/energy-dissipation","display_name":"energy dissipation","score":0.7400000095367432},{"id":"https://openalex.org/keywords/local-energy-inequality","display_name":"local energy inequality","score":0.9900000095367432},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"kinetic energy","score":0.4830000102519989},{"id":"https://openalex.org/keywords/besov-spaces","display_name":"Besov spaces","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7755488157272339},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.5914345383644104},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5773194432258606},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5563390851020813},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5336637496948242},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5136494040489197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5086548924446106},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5006880760192871},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43720743060112},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4290945529937744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33841803669929504},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18072518706321716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.047081053256988525},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.4007/annals.2026.204.1.4","doi":"https://doi.org/10.4007/annals.2026.204.1.4","is_oa":false,"landing_page_url":"https://doi.org/10.4007/annals.2026.204.1.4","pdf_url":null,"source":{"id":"https://openalex.org/S45918994","display_name":"Annals of Mathematics","issn_l":"0003-486X","issn":["0003-486X","1939-8980"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310316273","host_organization_name":"Princeton University","host_organization_lineage":["https://openalex.org/P4310316273"],"host_organization_lineage_names":["Princeton University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2305.18509","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.18509","pdf_url":"https://arxiv.org/pdf/2305.18509","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2305.18509","doi":"https://doi.org/10.48550/arxiv.2305.18509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2305.18509","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2305.18509","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.18509","pdf_url":"https://arxiv.org/pdf/2305.18509","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4378942455.pdf","grobid_xml":"https://content.openalex.org/works/W4378942455.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4313595893"],"related_works":["https://openalex.org/W2516843855","https://openalex.org/W2585552581","https://openalex.org/W2038955955","https://openalex.org/W7095599817","https://openalex.org/W4417299478","https://openalex.org/W4322099843","https://openalex.org/W1971209224","https://openalex.org/W2952724437","https://openalex.org/W4402505176","https://openalex.org/W7095309253"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,48],"prove":[4],"the":[5,11,26,31,54],"$L^3$-based":[6],"strong":[7],"Onsager":[8],"conjecture":[9],"for":[10,44],"three-dimensional":[12],"Euler":[13],"equations.":[14],"Our":[15],"main":[16],"theorem":[17],"states":[18],"that":[19],"there":[20],"exist":[21],"weak":[22],"solutions":[23,52],"which":[24],"dissipate":[25],"total":[27],"kinetic":[28],"energy,":[29],"satisfy":[30],"local":[32],"energy":[33],"inequality,":[34],"and":[35],"belong":[36],"to":[37],"$C^0_t":[38,56],"(W^{\\frac{1}{3},-3}":[39],"\\cap":[40,58],"L^{\\infty-})$.":[41],"More":[42],"precisely,":[43],"every":[45],"$\\beta\\lt":[46],"\\frac{1}{3}$,":[47],"can":[49],"construct":[50],"such":[51],"in":[53],"space":[55],"(B^\\beta_{3,\\infty}":[57],"L^{\\frac{1}{1-3\\beta}})$.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":17},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-06-01T00:00:00"}