{"id":"https://openalex.org/W7203745964","doi":"https://doi.org/10.48550/arxiv.2608.17383","title":"Compactly Supported Finite-Energy Stationary Solutions of the Three-Dimensional Navier-Stokes Equations","display_name":"Compactly Supported Finite-Energy Stationary Solutions of the Three-Dimensional Navier-Stokes Equations","publication_year":2026,"publication_date":"2026-08-18","ids":{"openalex":"https://openalex.org/W7203745964","doi":"https://doi.org/10.48550/arxiv.2608.17383"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.17383","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17383","pdf_url":"https://arxiv.org/pdf/2608.17383","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/2608.17383","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044177159","display_name":"Xuezhi Zhao","orcid":"https://orcid.org/0000-0002-6057-7237","observed_orcids":["https://orcid.org/0000-0002-6057-7237"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhao, Xuanxuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5044177159"],"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":0.9990000128746033,"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":0.9990000128746033,"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":9.999999747378752e-05,"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":9.999999747378752e-05,"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/stationary-navier-stokes-equations","display_name":"stationary Navier-Stokes equations","score":0.7950000166893005},{"id":"https://openalex.org/keywords/compactly-supported-solutions","display_name":"compactly supported solutions","score":0.8999999761581421},{"id":"https://openalex.org/keywords/distributional-solutions","display_name":"distributional solutions","score":0.6179999709129333},{"id":"https://openalex.org/keywords/three-dimensional-incompressible-flow","display_name":"three-dimensional incompressible flow","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6674000024795532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5164999961853027},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5145000219345093},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4611000120639801},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.35260000824928284},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33570000529289246},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.27489998936653137}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.17383","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17383","pdf_url":"https://arxiv.org/pdf/2608.17383","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.2608.17383","doi":"https://doi.org/10.48550/arxiv.2608.17383","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.17383","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:2608.17383","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.17383","pdf_url":"https://arxiv.org/pdf/2608.17383","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/W7203745964.pdf","grobid_xml":"https://content.openalex.org/works/W7203745964.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1966200801","https://openalex.org/W2090569969","https://openalex.org/W2911543757","https://openalex.org/W3027935030","https://openalex.org/W7099996896","https://openalex.org/W1213504496","https://openalex.org/W2767083885","https://openalex.org/W2416434424","https://openalex.org/W4410293427","https://openalex.org/W597132654"],"abstract_inverted_index":{"We":[0,115],"construct":[1],"nonzero":[2,80],"compactly":[3,18],"supported":[4,19],"stationary":[5,81],"distributional":[6],"solutions":[7,82],"$u\\in":[8],"L^2(\\mathbb{R}^3;\\mathbb{R}^3)$":[9],"of":[10,109],"the":[11,31,37,48,87,123,134],"unforced":[12],"incompressible":[13],"Navier--Stokes":[14],"equations,":[15],"together":[16],"with":[17,23],"pressures":[20],"in":[21,86,96],"$L^1$,":[22],"both":[24],"norms":[25],"arbitrarily":[26],"small.":[27],"The":[28,50,73],"construction":[29,124],"addresses":[30],"three-dimensional":[32],"finite-energy":[33],"endpoint":[34],"at":[35,101],"which":[36],"usual":[38],"single-scale":[39],"intermittent":[40],"Mikado":[41,57],"mechanism":[42,132],"loses":[43],"its":[44],"algebraic":[45],"gain":[46],"against":[47],"Laplacian.":[49],"main":[51],"new":[52],"ingredient":[53],"is":[54],"a":[55,61,77,129],"logarithmic":[56],"profile,":[58],"built":[59],"from":[60],"truncated":[62],"two-dimensional":[63],"harmonic":[64],"dipole":[65],"and":[66,95,98,127],"spread":[67],"over":[68],"logarithmically":[69],"many":[70],"transverse":[71],"scales.":[72],"same":[74],"perturbation":[75],"yields":[76],"localized":[78,88],"$h$-principle:":[79],"are":[83],"strongly":[84],"dense":[85,100],"$L^p$":[89],"classes":[90],"for":[91,133],"every":[92],"$1\\leq":[93],"p<2$":[94],"$H^{-1}$,":[97],"weakly":[99],"$p=2$,":[102],"while":[103],"strong":[104],"$L^2$":[105,120],"density":[106],"fails":[107],"because":[108],"an":[110],"exact":[111],"isotropic":[112],"quadratic-moment":[113],"constraint.":[114],"also":[116],"prescribe":[117],"arbitrary":[118],"positive":[119],"norms,":[121],"periodize":[122],"to":[125],"$\\mathbb{T}^3$,":[126],"obtain":[128],"stationary-versus-Leray":[130],"nonuniqueness":[131],"evolutionary":[135],"equations.":[136]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-20T00:00:00"}
