{"id":"https://openalex.org/W7214655674","doi":"https://doi.org/10.48550/arxiv.2609.31369","title":"Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise","display_name":"Convergence of a fully discrete approximation for the stochastic 2D Euler equations with Kraichnan transport noise","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214655674","doi":"https://doi.org/10.48550/arxiv.2609.31369"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31369","pdf_url":"https://arxiv.org/pdf/2609.31369","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/2609.31369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153216062","display_name":"Abhishek Chaudhary","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Chaudhary, Abhishek","raw_affiliation_strings":["Mathematisches Institut , Universit\u00e4t T\u00fcbingen , Auf der Morgenstelle 10 , D-72076 T\u00fcbingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Universit\u00e4t T\u00fcbingen , Auf der Morgenstelle 10 , D-72076 T\u00fcbingen , Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043451401","display_name":"Ujjwal Koley","orcid":"https://orcid.org/0000-0003-4455-8818","observed_orcids":["https://orcid.org/0000-0003-4455-8818"]},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]},{"id":"https://openalex.org/I94595606","display_name":"TIFR Centre for Applicable Mathematics","ror":"https://ror.org/00dp5a155","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468","https://openalex.org/I94595606"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Koley, Ujjwal","raw_affiliation_strings":["TIFR Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bengaluru , Karnataka 560065 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TIFR Centre for Applicable Mathematics , Tata Institute of Fundamental Research , Bengaluru , Karnataka 560065 , India","institution_ids":["https://openalex.org/I11947397","https://openalex.org/I94595606"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046668672","display_name":"Andreas Prohl","orcid":"https://orcid.org/0000-0003-4523-9536","observed_orcids":["https://orcid.org/0000-0003-4523-9536"]},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Prohl, Andreas","raw_affiliation_strings":["Mathematisches Institut , Universit\u00e4t T\u00fcbingen , Auf der Morgenstelle 10 , D-72076 T\u00fcbingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Universit\u00e4t T\u00fcbingen , Auf der Morgenstelle 10 , D-72076 T\u00fcbingen , Germany","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.9911999702453613,"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":0.9911999702453613,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0019000000320374966,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00139999995008111,"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/stochastic-euler-equations","display_name":"stochastic Euler equations","score":0.8220000267028809},{"id":"https://openalex.org/keywords/two-dimensional-incompressible-flow","display_name":"two-dimensional incompressible flow","score":0.8100000023841858},{"id":"https://openalex.org/keywords/vorticity-formulation","display_name":"vorticity formulation","score":0.8880000114440918},{"id":"https://openalex.org/keywords/fully-discrete-approximation","display_name":"fully discrete approximation","score":0.9399999976158142},{"id":"https://openalex.org/keywords/coercivity-estimates","display_name":"coercivity estimates","score":0.7310000061988831},{"id":"https://openalex.org/keywords/weak-martingale-solutions","display_name":"weak martingale solutions","score":0.7329999804496765},{"id":"https://openalex.org/keywords/compactness-estimates","display_name":"compactness estimates","score":0.5370000004768372}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6891999840736389},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6444000005722046},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5965999960899353},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5554999709129333},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.5325000286102295},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5148000121116638},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.49970000982284546},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4821000099182129},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4771000146865845},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.46070000529289246},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.41359999775886536},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.38370001316070557},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.3700999915599823},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.36010000109672546},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.3075000047683716},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.29989999532699585},{"id":"https://openalex.org/C13487092","wikidata":"https://www.wikidata.org/wiki/Q5282061","display_name":"Discrete spectrum","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2621999979019165},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31369","pdf_url":"https://arxiv.org/pdf/2609.31369","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.2609.31369","doi":"https://doi.org/10.48550/arxiv.2609.31369","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31369","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:2609.31369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31369","pdf_url":"https://arxiv.org/pdf/2609.31369","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214655674.pdf","grobid_xml":"https://content.openalex.org/works/W7214655674.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4300860212","https://openalex.org/W2944296117","https://openalex.org/W2791817682","https://openalex.org/W4385681600","https://openalex.org/W7123321045","https://openalex.org/W7165745163","https://openalex.org/W3014031886","https://openalex.org/W3036809013","https://openalex.org/W4416888428","https://openalex.org/W4404347953"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,33,59,86],"fully":[3],"discrete":[4,46,70],"approximation":[5],"theory":[6],"for":[7,37],"the":[8,38,45,48,53,78,91],"two-dimensional":[9],"incompressible":[10],"Euler":[11,92],"equations":[12],"on":[13,64],"$\\mathbb{T}^{2}$,":[14],"in":[15],"vorticity":[16],"form,":[17],"driven":[18],"by":[19,52],"Kraichnan-type":[20],"transport":[21,55],"noise":[22],"and":[23,68,80],"with":[24,58],"$\\mathbb{H}^{-1}(\\mathbb{T}^2)$-valued":[25],"initial":[26],"vorticity.":[27],"The":[28],"main":[29],"new":[30,60],"ingredient":[31],"is":[32,85],"finite-dimensional":[34],"coercivity":[35,73],"estimate":[36,74],"torus":[39],"Kraichnan":[40],"model,":[41],"which":[42],"captures":[43],"at":[44],"level":[47],"regularizing":[49],"mechanism":[50],"induced":[51],"rough":[54],"noise.":[56],"Together":[57],"compactness":[61],"strategy":[62],"based":[63],"continuous":[65],"equation-based":[66],"interpolants":[67],"localized":[69],"estimates,":[71],"this":[72],"gives":[75],"tightness":[76],"of":[77,90],"approximations":[79],"shows":[81],"that":[82],"subsequential":[83],"limit":[84],"weak":[87],"martingale":[88],"solution":[89],"equations.":[93]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-29T00:00:00"}