{"id":"https://openalex.org/W7204934849","doi":"https://doi.org/10.48550/arxiv.2608.30582","title":"A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains","display_name":"A stochastic convex integration scheme for the intermittent Onsager theorem in two-dimensional domains","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204934849","doi":"https://doi.org/10.48550/arxiv.2608.30582"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30582","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30582","pdf_url":"https://arxiv.org/pdf/2608.30582","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30582","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148868278","display_name":"Zhenxin Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zhenxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052870632","display_name":"Wenhu Zhong","orcid":"https://orcid.org/0000-0003-1666-8075","observed_orcids":["https://orcid.org/0000-0003-1666-8075"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong, Wenhu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9951000213623047,"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":0.9951000213623047,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.0010999999940395355,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.0003000000142492354,"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/martingale-solutions","display_name":"martingale solutions","score":0.9380000233650208},{"id":"https://openalex.org/keywords/holder-continuity","display_name":"H\u00f6lder continuity","score":0.8450000286102295},{"id":"https://openalex.org/keywords/intermittency","display_name":"intermittency","score":0.9010000228881836},{"id":"https://openalex.org/keywords/dissipative-solutions","display_name":"dissipative solutions","score":0.7059999704360962},{"id":"https://openalex.org/keywords/littlewood-paley-decomposition","display_name":"Littlewood-Paley decomposition","score":0.9890000224113464},{"id":"https://openalex.org/keywords/reynolds-stress","display_name":"Reynolds stress","score":0.9449999928474426},{"id":"https://openalex.org/keywords/two-dimensional-hydrodynamics","display_name":"two-dimensional fluid dynamics","score":0.628000020980835}],"concepts":[{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.7052000164985657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6974999904632568},{"id":"https://openalex.org/C2780388094","wikidata":"https://www.wikidata.org/wiki/Q1666248","display_name":"Intermittency","level":3,"score":0.5586000084877014},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5175999999046326},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5085999965667725},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.47760000824928284},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4077000021934509},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40450000762939453},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.3978999853134155},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.3246000111103058},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.3009999990463257},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.2696000039577484}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30582","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30582","pdf_url":"https://arxiv.org/pdf/2608.30582","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30582","doi":"https://doi.org/10.48550/arxiv.2608.30582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30582","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30582","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30582","pdf_url":"https://arxiv.org/pdf/2608.30582","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G322682455","display_name":null,"funder_award_id":"11925102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4060397366","display_name":null,"funder_award_id":"12171343","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G522012478","display_name":null,"funder_award_id":"12531009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204934849.pdf","grobid_xml":"https://content.openalex.org/works/W7204934849.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4407632638","https://openalex.org/W4417299478"],"related_works":["https://openalex.org/W4322099843","https://openalex.org/W4417299478","https://openalex.org/W4401202673","https://openalex.org/W2079505476","https://openalex.org/W7024916550","https://openalex.org/W7101010586","https://openalex.org/W2213565566","https://openalex.org/W4403112672","https://openalex.org/W2058440918","https://openalex.org/W3080801352"],"abstract_inverted_index":{"For":[0],"any":[1],"$\u03b3\\in":[2],"\\left[":[3],"{0,\\frac{1}{3}}":[4],"\\right)$,":[5],"we":[6],"construct":[7],"$\u03b3$-H\u00f6lder-continuous":[8],"martingale":[9,19],"solutions":[10,20],"to":[11,68],"the":[12,28,32,46,51,70],"two-dimensional":[13],"stochastic":[14,41,61,71],"incompressible":[15],"Euler":[16],"equations.":[17],"These":[18],"exhibit":[21],"dissipative":[22],"behavior":[23],"and":[24,42,65,72],"intermittency,":[25],"thereby":[26],"establishing":[27],"flexible":[29],"part":[30],"of":[31,45],"intermittent":[33,43,66,73],"Onsager":[34],"theorem.":[35],"The":[36],"proof":[37],"rests":[38],"on":[39],"a":[40],"variant":[44],"Newton--Nash":[47],"iteration":[48,57],"combined":[49],"with":[50],"Littlewood--Paley":[52],"decomposition":[53],"scheme.":[54],"This":[55],"composite":[56],"scheme":[58],"incorporates":[59],"new":[60],"pressure,":[62],"Reynolds":[63],"stress":[64],"perturbations":[67],"formalize":[69],"fluctuations.":[74]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}