{"id":"https://openalex.org/W7204909102","doi":"https://doi.org/10.48550/arxiv.2608.29664","title":"Critical Morrey Rigidity and Removable Singularities for Five-Dimensional Stationary Navier-Stokes Flows","display_name":"Critical Morrey Rigidity and Removable Singularities for Five-Dimensional Stationary Navier-Stokes Flows","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204909102","doi":"https://doi.org/10.48550/arxiv.2608.29664"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29664","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29664","pdf_url":"https://arxiv.org/pdf/2608.29664","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/2608.29664","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101939526","display_name":"Yubo Chen","orcid":"https://orcid.org/0000-0002-9862-4094","observed_orcids":["https://orcid.org/0000-0002-9862-4094","https://orcid.org/0000-0002-2322-2349"]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Yubo","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5145949160","display_name":"Wendong Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Wendong","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148882949","display_name":"Xiao Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Xiao","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113849047","display_name":"Guoxu Yang","orcid":"https://orcid.org/0009-0001-5926-5105","observed_orcids":["https://orcid.org/0009-0001-5926-5105"]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Guoxu","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114310348","display_name":"Jianbo Yu","orcid":"https://orcid.org/0009-0001-2899-1446","observed_orcids":["https://orcid.org/0009-0001-2899-1446"]},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu, Jianbo","raw_affiliation_strings":["School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Dalian University of Technology , Dalian 116024 , China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.00279999990016222,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00039999998989515007,"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":0.8790000081062317},{"id":"https://openalex.org/keywords/removable-singularities","display_name":"removable singularities","score":0.878000020980835},{"id":"https://openalex.org/keywords/head-pressure","display_name":"head pressure","score":0.5600000023841858},{"id":"https://openalex.org/keywords/isolated-singularities","display_name":"isolated singularities","score":0.800000011920929},{"id":"https://openalex.org/keywords/regularity-criteria","display_name":"regularity criteria","score":0.6110000014305115},{"id":"https://openalex.org/keywords/suitable-weak-solutions","display_name":"suitable weak solutions","score":0.5320000052452087}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7660999894142151},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.723800003528595},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6933000087738037},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6741999983787537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6467999815940857},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6100000143051147},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6039000153541565},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4968999922275543},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.2937000095844269},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2858000099658966},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.2565000057220459},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29664","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29664","pdf_url":"https://arxiv.org/pdf/2608.29664","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.2608.29664","doi":"https://doi.org/10.48550/arxiv.2608.29664","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29664","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:2608.29664","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29664","pdf_url":"https://arxiv.org/pdf/2608.29664","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/W7204909102.pdf","grobid_xml":"https://content.openalex.org/works/W7204909102.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4415434120"],"related_works":["https://openalex.org/W2004128028","https://openalex.org/W4415434120","https://openalex.org/W7214087722","https://openalex.org/W2024629248","https://openalex.org/W4414384943","https://openalex.org/W2092731604","https://openalex.org/W2007993400","https://openalex.org/W2079324586","https://openalex.org/W1993167847","https://openalex.org/W1877788796"],"abstract_inverted_index":{"We":[0,77,183],"prove":[1,185],"a":[2,49,61,79,86,126,133,197],"critical":[3],"Morrey":[4,153,190],"rigidity":[5,46,191],"theorem":[6,192],"for":[7,89],"the":[8,34,38,43,83,90,115,161,167,170,174,186],"five-dimensional":[9],"stationary":[10,176],"Navier--Stokes":[11],"equations.":[12],"More":[13],"precisely,":[14],"every":[15],"smooth":[16,138],"solution":[17,136],"on":[18,69],"$\\mathbb":[19],"R^5\\setminus\\{0\\}$":[20],"satisfying":[21],"\\[":[22],"\\sup_{R>0}R^{-2}\\int_{B_R}|u|^3\\,dx<\\infty":[23],"\\]":[24],"is":[25,137,163,179],"identically":[26],"zero,":[27],"up":[28],"to":[29,113],"an":[30,122],"additive":[31],"constant":[32],"in":[33,42,129,173,193],"pressure.":[35],"This":[36],"replaces":[37],"pointwise":[39,70],"Type-I":[40],"control":[41],"known":[44],"higher-dimensional":[45],"theory":[47],"by":[48,181,196],"velocity-only,":[50],"scale-invariant":[51,146],"averaged":[52],"condition":[53],"that":[54,65,158],"allows":[55],"spatial":[56],"concentration.":[57],"The":[58],"proof":[59],"develops":[60],"weak":[62,135],"head-pressure":[63],"mechanism":[64],"does":[66],"not":[67],"rely":[68],"pressure":[71,81],"estimates":[72],"or":[73,149],"classical":[74,175],"normal":[75],"traces.":[76],"reconstruct":[78],"canonical":[80],"from":[82,140],"velocity,":[84],"derive":[85],"renormalized":[87],"inequality":[88],"positive":[91],"head":[92],"pressure,":[93],"and":[94,105,107,118,143],"introduce":[95],"two":[96],"monotone":[97],"radial":[98],"fluxes.":[99],"Annular":[100],"energy":[101,148],"estimates,":[102],"suitable-weak":[103],"compactness,":[104],"blow-up":[106],"blow-down":[108],"limits":[109],"are":[110],"then":[111,160],"used":[112],"identify":[114],"endpoint":[116],"fluxes":[117],"force":[119],"rigidity.":[120],"As":[121],"application,":[123],"we":[124],"obtain":[125],"removable-singularity":[127],"criterion":[128,178],"dimension":[130,194],"five:":[131],"if":[132],"suitable":[134],"away":[139],"one":[141],"point":[142],"either":[144],"its":[145,150],"Dirichlet":[147],"cubic":[151,189],"velocity":[152],"quantity":[154],"remains":[155],"bounded":[156],"near":[157],"point,":[159],"singularity":[162],"removable.":[164],"Thus,":[165],"within":[166],"isolated-singularity":[168],"class,":[169],"smallness":[171],"assumption":[172],"regularity":[177],"replaced":[180],"boundedness.":[182],"also":[184],"corresponding":[187],"velocity-only":[188],"four":[195],"different":[198],"finite-energy":[199],"argument.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
