{"id":"https://openalex.org/W4412469102","doi":"https://doi.org/10.3390/sym17071138","title":"Local and Global Solutions of the 3D-NSE in Homogeneous Lei\u2013Lin\u2013Gevrey Spaces","display_name":"Local and Global Solutions of the 3D-NSE in Homogeneous Lei\u2013Lin\u2013Gevrey Spaces","publication_year":2025,"publication_date":"2025-07-16","ids":{"openalex":"https://openalex.org/W4412469102","doi":"https://doi.org/10.3390/sym17071138"},"language":"en","primary_location":{"id":"doi:10.3390/sym17071138","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17071138","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/sym17071138","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019701034","display_name":"Lotfi Jlali","orcid":"https://orcid.org/0000-0001-7604-0955"},"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"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Lotfi Jlali","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019701034"],"corresponding_institution_ids":["https://openalex.org/I240666556"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.8972,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95556032,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"17","issue":"7","first_page":"1138","last_page":"1138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9934999942779541,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6973903775215149},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5436884164810181},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45261436700820923},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4294429421424866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4213978946208954},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3255038261413574},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19533193111419678}],"concepts":[{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6973903775215149},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5436884164810181},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45261436700820923},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4294429421424866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4213978946208954},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3255038261413574},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19533193111419678}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17071138","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17071138","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17071138","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17071138","pdf_url":null,"source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1973779621","https://openalex.org/W1982418511","https://openalex.org/W2043876702","https://openalex.org/W2078362444","https://openalex.org/W2167967599","https://openalex.org/W2412676986","https://openalex.org/W2528949860","https://openalex.org/W3056766378"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0,119],"paper":[1],"investigates":[2],"the":[3,13,19,34,39,43,66,73,94,106,111],"existence":[4],"and":[5,9,28,57,81,128,133],"uniqueness":[6],"of":[7,21,38,46,54,68,105,114,126],"local":[8],"global":[10],"solutions":[11,99,115],"to":[12,122],"incompressible":[14],"three-dimensional":[15],"Navier\u2013Stokes":[16,95],"equations":[17],"within":[18],"framework":[20],"homogeneous":[22],"Lei\u2013Lin\u2013Gevrey":[23],"spaces":[24,32,41],"Xa,\u03b3\u03c1(R3),":[25],"where":[26],"\u03c1\u2208[\u22121,0),a&gt;0,":[27],"\u03b3\u2208(0,1).":[29],"These":[30],"function":[31],"combine":[33],"critical":[35,74,132],"scaling":[36],"structure":[37],"Lei\u2013Lin":[40,75],"with":[42],"exponential":[44],"regularity":[45,56,83,127],"Gevrey":[47,107],"classes,":[48],"thereby":[49],"enabling":[50],"a":[51,123],"refined":[52],"treatment":[53],"analytic":[55],"frequency":[58],"localization.":[59],"The":[60,103],"main":[61],"results":[62],"are":[63],"obtained":[64],"under":[65],"assumption":[67],"small":[69],"initial":[70,92],"data":[71],"in":[72,101,131],"space":[76],"X\u03c1(R3),":[77],"extending":[78],"previous":[79],"works":[80],"improving":[82],"thresholds.":[84],"In":[85],"particular,":[86],"we":[87],"establish":[88],"that":[89],"for":[90],"suitable":[91],"data,":[93],"system":[96],"admits":[97],"unique":[98],"globally":[100],"time.":[102],"influence":[104],"parameter":[108],"\u03b3":[109],"on":[110],"high-frequency":[112],"behavior":[113],"is":[116],"also":[117],"discussed.":[118],"work":[120],"contributes":[121],"deeper":[124],"understanding":[125],"decay":[129],"properties":[130],"supercritical":[134],"regimes.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-06-03T09:05:47.796612","created_date":"2025-10-10T00:00:00"}
