{"id":"https://openalex.org/W7213266754","doi":"https://doi.org/10.48550/arxiv.2609.14292","title":"A compatibility--realization framework for singular Navier--Stokes flows: admissible families and non-rigid core mechanics","display_name":"A compatibility--realization framework for singular Navier--Stokes flows: admissible families and non-rigid core mechanics","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213266754","doi":"https://doi.org/10.48550/arxiv.2609.14292"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14292","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14292","pdf_url":"https://arxiv.org/pdf/2609.14292","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/2609.14292","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102737223","display_name":"Weishuo Liu","orcid":"https://orcid.org/0000-0001-9257-0817","observed_orcids":["https://orcid.org/0000-0001-9257-0817"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liu, Weishuo","raw_affiliation_strings":["School of Mechanics and Engineering Science Peking University , Beijing 100871 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanics and Engineering Science Peking University , Beijing 100871 , China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102737223"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"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":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"}},{"id":"https://openalex.org/T13951","display_name":"Fluid dynamics and aerodynamics studies","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"}}],"keywords":[{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/singular-solutions","display_name":"singular solutions","score":0.9129999876022339},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"incompressible flow","score":0.7289999723434448},{"id":"https://openalex.org/keywords/three-dimensional-flow","display_name":"three-dimensional flow","score":0.6230000257492065},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.7429999709129333},{"id":"https://openalex.org/keywords/vorticity-balance","display_name":"vorticity balance","score":0.5820000171661377},{"id":"https://openalex.org/keywords/axisymmetric-flow","display_name":"axisymmetric flow","score":0.5960000157356262},{"id":"https://openalex.org/keywords/right-inverses","display_name":"right inverses","score":0.6449999809265137},{"id":"https://openalex.org/keywords/analytic-perturbations","display_name":"analytic perturbations","score":0.5669999718666077}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7401000261306763},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.579200029373169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5350000262260437},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.5296000242233276},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.39419999718666077},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31189998984336853},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2971000075340271},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.28290000557899475},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14292","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14292","pdf_url":"https://arxiv.org/pdf/2609.14292","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.2609.14292","doi":"https://doi.org/10.48550/arxiv.2609.14292","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14292","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:2609.14292","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14292","pdf_url":"https://arxiv.org/pdf/2609.14292","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/W7213266754.pdf","grobid_xml":"https://content.openalex.org/works/W7213266754.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7212168829","https://openalex.org/W7222961759","https://openalex.org/W2982320097","https://openalex.org/W7098144987","https://openalex.org/W7213308499","https://openalex.org/W7212849874","https://openalex.org/W7213594155","https://openalex.org/W2991217998","https://openalex.org/W7172394812","https://openalex.org/W3080372436"],"abstract_inverted_index":{"We":[0,164],"introduce":[1],"a":[2,26,35,87,101,105,116,131,139],"compatibility--realization":[3],"framework":[4,17],"for":[5],"constructing":[6],"singular":[7,107],"solutions":[8],"to":[9],"the":[10,31,51,59,121,134,152,158,167,176,181,201,224],"forced":[11],"three-dimensional":[12],"incompressible":[13],"Navier--Stokes":[14],"equations.":[15],"The":[16,185],"separates":[18],"exact":[19],"balance":[20,161],"and":[21,54,81,97,115,148,157,170,192,208],"matching":[22],"constraints,":[23],"expressed":[24],"in":[25,64,141,180],"chosen":[27,182],"geometric":[28],"representation,":[29],"from":[30,50],"sufficient":[32],"conditions":[33],"of":[34,89,123,145,175,217,223],"particular":[36],"completion":[37,61],"scheme.":[38],"Completed":[39],"realizations":[40],"are":[41,212],"organized":[42],"by":[43],"observable":[44,190],"fibers,":[45],"distinguishing":[46],"prescribed":[47],"core":[48],"kinematics":[49,196],"surrounding":[52],"force":[53],"transport":[55],"mechanisms.":[56],"Conditional":[57],"on":[58],"source-dependent":[60],"input":[62],"specified":[63],"this":[65],"paper,":[66],"we":[67],"obtain":[68],"families":[69],"with":[70],"zero":[71,124],"initial":[72],"velocity,":[73],"smooth":[74],"compactly":[75],"supported":[76],"forcing,":[77],"bounded":[78],"kinetic":[79],"energy":[80],"finite-time":[82],"unbounded":[83],"velocity.":[84],"These":[85],"include":[86],"reversal":[88],"leading":[90,125],"viscous":[91,127],"work":[92],"at":[93],"fixed":[94,111],"axis":[95,195],"motion":[96],"first":[98,154],"velocity":[99,155],"gradient,":[100],"signed":[102],"transition":[103],"through":[104],"stationary":[106],"center":[108],"under":[109],"one":[110],"canonical":[112],"pressure":[113,149],"trace,":[114],"connected":[117],"stretching":[118],"family":[119],"crossing":[120],"threshold":[122],"direct":[126],"vorticity":[128,160],"supply.":[129],"Near":[130],"critical":[132,159],"profile,":[133],"realizable":[135],"trace":[136],"data":[137],"contain":[138],"neighborhood":[140],"an":[142,171],"infinite-dimensional":[143],"space":[144],"analytic":[146],"axial-velocity":[147],"perturbations,":[150],"while":[151],"central":[153],"gradient":[156],"remain":[162],"fixed.":[163],"also":[165],"identify":[166],"full":[168],"kernel":[169],"explicit":[172],"right":[173],"inverse":[174],"joint":[177],"angular-transport":[178],"operator":[179],"realization":[183],"class.":[184],"results":[186],"establish":[187],"non-rigidity":[188],"within":[189],"fibers":[191],"show":[193],"that":[194],"alone":[197],"do":[198],"not":[199],"determine":[200],"local":[202],"pressure--viscosity":[203],"partition.":[204],"Direct":[205],"profile":[206],"selection":[207],"dynamical":[209],"stress":[210],"generation":[211],"treated":[213],"as":[214,221],"coupled":[215],"components":[216],"construction,":[218],"rather":[219],"than":[220],"definitions":[222],"entire":[225],"design":[226],"space.":[227]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-16T00:00:00"}
