{"id":"https://openalex.org/W7214736998","doi":"https://doi.org/10.48550/arxiv.2609.32719","title":"Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces","display_name":"Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214736998","doi":"https://doi.org/10.48550/arxiv.2609.32719"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32719","pdf_url":"https://arxiv.org/pdf/2609.32719","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/2609.32719","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081298699","display_name":"Jamel Benameur","orcid":"https://orcid.org/0000-0002-6043-9037","observed_orcids":["https://orcid.org/0000-0002-6043-9037"]},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]},{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Benameur, Jamel","raw_affiliation_strings":["Department of Mathematics , College of Science , King Saud University (KSU) Riyadh 11451 , Saudi Arabia","Department of Mathematics and Statistics , College of Science , Imam Mohammad Ibn Saud Islamic University (IMSIU) Riyadh 11432 , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , College of Science , King Saud University (KSU) Riyadh 11451 , Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , College of Science , Imam Mohammad Ibn Saud Islamic University (IMSIU) Riyadh 11432 , Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019701034","display_name":"Lotfi Jlali","orcid":"https://orcid.org/0000-0001-7604-0955","observed_orcids":["https://orcid.org/0000-0001-7604-0955"]},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Jlali, Lotfi","raw_affiliation_strings":["Department of Mathematics , College of Science , King Saud University (KSU) Riyadh 11451 , Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , College of Science , King Saud University (KSU) Riyadh 11451 , Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/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/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.8180000185966492},{"id":"https://openalex.org/keywords/blow-up-criterion","display_name":"blow-up criterion","score":0.675000011920929},{"id":"https://openalex.org/keywords/nonlinear-damping","display_name":"nonlinear damping","score":0.671999990940094},{"id":"https://openalex.org/keywords/local-existence-and-uniqueness","display_name":"local existence and uniqueness","score":0.718999981880188},{"id":"https://openalex.org/keywords/maximal-solutions","display_name":"maximal solutions","score":0.7820000052452087},{"id":"https://openalex.org/keywords/three-dimensional-incompressible-flow","display_name":"three-dimensional incompressible flow","score":0.9269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8084999918937683},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6862999796867371},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6859999895095825},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6159999966621399},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5351999998092651},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5182999968528748},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4943000078201294},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.4609000086784363},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3644999861717224},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.34439998865127563},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.32010000944137573},{"id":"https://openalex.org/C50826107","wikidata":"https://www.wikidata.org/wiki/Q5475803","display_name":"Fourier transform on finite groups","level":5,"score":0.3197000026702881},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.25780001282691956},{"id":"https://openalex.org/C103642545","wikidata":"https://www.wikidata.org/wiki/Q5421531","display_name":"Exponential type","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32719","pdf_url":"https://arxiv.org/pdf/2609.32719","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.2609.32719","doi":"https://doi.org/10.48550/arxiv.2609.32719","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32719","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:2609.32719","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32719","pdf_url":"https://arxiv.org/pdf/2609.32719","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/W7214736998.pdf","grobid_xml":"https://content.openalex.org/works/W7214736998.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7160610807","https://openalex.org/W2798921675","https://openalex.org/W2969687584","https://openalex.org/W3005654839","https://openalex.org/W2789923686","https://openalex.org/W3007380273","https://openalex.org/W2962947172","https://openalex.org/W7214755602","https://openalex.org/W2977425274","https://openalex.org/W2436744075"],"abstract_inverted_index":{"We":[0,27,43],"study":[1],"the":[2,14,38,49,70,81,94],"three-dimensional":[3],"incompressible":[4],"Navier--Stokes":[5],"equations":[6],"with":[7],"a":[8,58,65,73,89],"componentwise":[9],"nonlinear":[10],"damping":[11],"term":[12],"of":[13,34,83],"form":[15],"$\u03b1\\sum_{k=1}^3":[16],"u_k^{2m+1}e_k$":[17],"in":[18,48,57,93],"Fourier":[19,96],"and":[20,32,36],"Fourier--":[21],"Gevrey":[22],"spaces":[23],"based":[24],"on":[25],"$\\mathcal{X}^0(\\mathbb{R}^3)$.":[26,98],"first":[28],"establish":[29,64],"local-in-time":[30],"existence":[31,77],"uniqueness":[33],"solutions":[35],"obtain":[37,88],"corresponding":[39,90],"unique":[40],"maximal":[41,76],"solutions.":[42],"then":[44],"derive":[45],"blow-up":[46,55],"criteria":[47],"Fourier--Gevrey":[50],"framework,":[51],"including":[52],"an":[53],"integral":[54],"criterion":[56],"weaker":[59],"exponential":[60,84],"weight.":[61],"Moreover,":[62],"we":[63,86],"quantitative":[66],"lower":[67,91],"bound":[68,92],"for":[69],"solution":[71],"near":[72],"possible":[74],"finite":[75],"time.":[78],"By":[79],"iterating":[80],"loss":[82],"weight,":[85],"finally":[87],"unweighted":[95],"space":[97]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-30T00:00:00"}
