{"id":"https://openalex.org/W7220409167","doi":"https://doi.org/10.48550/arxiv.2610.02509","title":"Finite-time blowup of the Euler equation without forcing","display_name":"Finite-time blowup of the Euler equation without forcing","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7220409167","doi":"https://doi.org/10.48550/arxiv.2610.02509"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02509","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02509","pdf_url":"https://arxiv.org/pdf/2610.02509","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.02509","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102882403","display_name":"Fan Zheng","orcid":"https://orcid.org/0000-0002-5718-4010","observed_orcids":["https://orcid.org/0000-0002-5718-4010"]},"institutions":[{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Zheng, Fan","raw_affiliation_strings":["Instituto de Ciencias Matem\u00e1ticas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias Matem\u00e1ticas","institution_ids":["https://openalex.org/I4210157032"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102882403"],"corresponding_institution_ids":["https://openalex.org/I4210157032"],"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":0.9961000084877014,"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":0.9961000084877014,"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":0.0019000000320374966,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.0003000000142492354,"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/euler-equations","display_name":"Euler equations","score":0.9049999713897705},{"id":"https://openalex.org/keywords/finite-time-blow-up","display_name":"finite-time blow-up","score":0.949999988079071},{"id":"https://openalex.org/keywords/three-dimensional-incompressible-flow","display_name":"three-dimensional incompressible flow","score":0.8960000276565552},{"id":"https://openalex.org/keywords/smooth-solutions","display_name":"smooth solutions","score":0.48399999737739563},{"id":"https://openalex.org/keywords/singularity-formation","display_name":"singularity formation","score":0.43799999356269836}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.652999997138977},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5867000222206116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5697000026702881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5680999755859375},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.4948999881744385},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.41929998993873596},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.39309999346733093},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3610999882221222},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C2781217745","wikidata":"https://www.wikidata.org/wiki/Q1053779","display_name":"Euler system","level":3,"score":0.28859999775886536},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02509","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02509","pdf_url":"https://arxiv.org/pdf/2610.02509","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.2610.02509","doi":"https://doi.org/10.48550/arxiv.2610.02509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02509","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:2610.02509","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02509","pdf_url":"https://arxiv.org/pdf/2610.02509","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220409167.pdf","grobid_xml":"https://content.openalex.org/works/W7220409167.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7096481019","https://openalex.org/W2325008123","https://openalex.org/W2883949042","https://openalex.org/W1485915739","https://openalex.org/W4386839789","https://openalex.org/W2610500921","https://openalex.org/W7213341086","https://openalex.org/W7212281639","https://openalex.org/W2953818507","https://openalex.org/W2155805795"],"abstract_inverted_index":{"These":[0],"notes":[1],"present":[2],"the":[3,11,50],"construction":[4,27],"in":[5],"\\cite{euler}":[6],"of":[7],"finite-time":[8],"blowup":[9],"for":[10],"three-dimensional":[12],"incompressible,":[13],"unforced":[14],"Euler":[15],"equations":[16],"on":[17],"$\\mathbb":[18],"R^3$:":[19],"\\begin{equation}":[20],"\\partial_tu+(u\\cdot\\nabla)u+\\nabla":[21],"p=0,\\qquad":[22],"\\nabla\\cdot":[23],"u=0.":[24],"\\end{equation}":[25],"The":[26],"successively":[28],"adds":[29],"oscillatory":[30],"layers":[31],"to":[32],"smooth":[33],"parent":[34],"solutions.":[35],"Each":[36],"layer":[37],"is":[38],"constructed":[39],"by":[40],"a":[41],"finite":[42],"expansion":[43],"and":[44],"an":[45],"exact":[46],"correction,":[47],"so":[48],"that":[49],"resulting":[51],"child":[52],"solves":[53],"Euler.":[54]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-06T00:00:00"}
