{"id":"https://openalex.org/W4318205985","doi":"https://doi.org/10.3390/sym15020343","title":"Existence of Global and Local Mild Solution for the Fractional Navier\u2013Stokes Equations","display_name":"Existence of Global and Local Mild Solution for the Fractional Navier\u2013Stokes Equations","publication_year":2023,"publication_date":"2023-01-26","ids":{"openalex":"https://openalex.org/W4318205985","doi":"https://doi.org/10.3390/sym15020343"},"language":"en","primary_location":{"id":"doi:10.3390/sym15020343","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15020343","pdf_url":"https://www.mdpi.com/2073-8994/15/2/343/pdf?version=1676634138","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","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/2/343/pdf?version=1676634138","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060006810","display_name":"Muath Awadalla","orcid":"https://orcid.org/0000-0002-6447-6361"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muath Awadalla","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6447-6361","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001000167","display_name":"Azhar Hussain","orcid":"https://orcid.org/0000-0003-4501-9269"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Azhar Hussain","raw_affiliation_strings":["Department Mathematics, University of Chakwal, Chakwal 48800, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-4501-9269","affiliations":[{"raw_affiliation_string":"Department Mathematics, University of Chakwal, Chakwal 48800, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024361190","display_name":"Farva Hafeez","orcid":null},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]},{"id":"https://openalex.org/I160968435","display_name":"University of Sargodha","ror":"https://ror.org/0086rpr26","country_code":"PK","type":"education","lineage":["https://openalex.org/I160968435"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Farva Hafeez","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Lahore, Sargodha 40100, Pakistan","institution_ids":["https://openalex.org/I160968435","https://openalex.org/I142204992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076378258","display_name":"Kinda Abuasbeh","orcid":"https://orcid.org/0000-0003-2744-6320"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Kinda Abuasbeh","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2744-6320","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001000167","https://openalex.org/A5060006810"],"corresponding_institution_ids":["https://openalex.org/I4626487"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6382,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.60913057,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"15","issue":"2","first_page":"343","last_page":"343"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/fractional-calculus","display_name":"Fractional calculus","score":0.7528663277626038},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6129825115203857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5503579378128052},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5481274127960205},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5466112494468689},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4849700927734375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4518361985683441},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4088180661201477},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33525797724723816},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.15676885843276978},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.08047154545783997},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06605780124664307}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7528663277626038},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6129825115203857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5503579378128052},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5481274127960205},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5466112494468689},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4849700927734375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4518361985683441},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4088180661201477},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33525797724723816},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.15676885843276978},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.08047154545783997},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06605780124664307},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15020343","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15020343","pdf_url":"https://www.mdpi.com/2073-8994/15/2/343/pdf?version=1676634138","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"},{"id":"pmh:oai:doaj.org/article:a7417d73f14545d28008c2d2c2f5e8f8","is_oa":false,"landing_page_url":"https://doaj.org/article/a7417d73f14545d28008c2d2c2f5e8f8","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 2, p 343 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/2/343/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15020343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15020343","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15020343","pdf_url":"https://www.mdpi.com/2073-8994/15/2/343/pdf?version=1676634138","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":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4318205985.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1550467807","https://openalex.org/W1987298665","https://openalex.org/W1993450117","https://openalex.org/W2034527816","https://openalex.org/W2045647581","https://openalex.org/W2058040466","https://openalex.org/W2069155430","https://openalex.org/W2070454382","https://openalex.org/W2078125833","https://openalex.org/W2078650615","https://openalex.org/W2145622768","https://openalex.org/W2343761172","https://openalex.org/W2527607239","https://openalex.org/W2593431222","https://openalex.org/W4236398741","https://openalex.org/W4301223505","https://openalex.org/W4304128277","https://openalex.org/W6623081871","https://openalex.org/W6662115159","https://openalex.org/W6704446060"],"related_works":["https://openalex.org/W4300711749","https://openalex.org/W2246967737","https://openalex.org/W2080482296","https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385"],"abstract_inverted_index":{"Navier\u2013Stokes":[0],"equations":[1,36,44],"(NS-equations)":[2],"are":[3,16],"applied":[4],"extensively":[5],"for":[6],"the":[7,14,23,26,54,59,67,74,85,99],"study":[8],"of":[9,29,87,101],"various":[10],"waves":[11],"phenomena":[12],"where":[13],"symmetries":[15],"involved.":[17],"In":[18,32],"this":[19],"paper,":[20],"we":[21,72],"discuss":[22],"NS-equations":[24],"with":[25],"time-fractional":[27],"derivative":[28],"order":[30],"\u03b2\u2208(0,1).":[31],"fractional":[33,69],"media,":[34],"these":[35],"can":[37,46],"be":[38,47],"utilized":[39],"to":[40,49,97],"recreate":[41],"anomalous":[42],"diffusion":[43],"which":[45],"used":[48],"construct":[50],"symmetries.":[51],"We":[52,82],"examine":[53],"initial":[55],"value":[56],"problem":[57],"involving":[58],"symmetric":[60],"Stokes":[61],"operator":[62],"and":[63,76],"gravitational":[64],"force":[65],"utilizing":[66],"Caputo":[68],"derivative.":[70],"Additionally,":[71],"demonstrate":[73,84,98],"global":[75],"local":[77],"mild":[78],"solutions":[79,89],"in":[80,90],"H\u03b1,p.":[81],"also":[83],"regularity":[86],"classical":[88],"such":[91],"circumstances.":[92],"An":[93],"example":[94],"is":[95],"presented":[96],"reliability":[100],"our":[102],"findings.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
