{"id":"https://openalex.org/W2902719448","doi":"https://doi.org/10.1137/19m1259900","title":"Regularity in Time of H\u00f6lder Solutions of Euler and Hypodissipative Navier--Stokes Equations","display_name":"Regularity in Time of H\u00f6lder Solutions of Euler and Hypodissipative Navier--Stokes Equations","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2902719448","doi":"https://doi.org/10.1137/19m1259900","mag":"2902719448"},"language":"en","primary_location":{"id":"doi:10.1137/19m1259900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1259900","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.12870","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065229312","display_name":"Maria Colombo","orcid":"https://orcid.org/0000-0003-3294-472X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Maria Colombo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5008915429","display_name":"Luigi De Rosa","orcid":"https://orcid.org/0000-0002-7157-5114"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luigi De Rosa","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065229312"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5848,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57940894,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"52","issue":"1","first_page":"221","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9901000261306763,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9794999957084656,"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/regularization","display_name":"Regularization (linguistics)","score":0.7057968974113464},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.6628651022911072},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.55190110206604},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5376203656196594},{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.5292367935180664},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4848857820034027},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4769779145717621},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.46455878019332886},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4527006149291992},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4414641857147217},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.43092644214630127},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.42928075790405273},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4238489866256714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39048242568969727},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2297368347644806},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.1387043595314026},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.13541260361671448},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.10416248440742493},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09127700328826904}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7057968974113464},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.6628651022911072},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.55190110206604},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5376203656196594},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.5292367935180664},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4848857820034027},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4769779145717621},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.46455878019332886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4527006149291992},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4414641857147217},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.43092644214630127},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.42928075790405273},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4238489866256714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39048242568969727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2297368347644806},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1387043595314026},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.13541260361671448},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.10416248440742493},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09127700328826904},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/19m1259900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1259900","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.12870","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.12870","pdf_url":"https://arxiv.org/pdf/1811.12870","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"mag:2902719448","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1811.12870","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:278805","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/278805","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},{"id":"doi:10.48550/arxiv.1811.12870","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.12870","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1811.12870","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.12870","pdf_url":"https://arxiv.org/pdf/1811.12870","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[{"display_name":"Affordable and clean energy","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G6041984722","display_name":null,"funder_award_id":"146349","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G964064198","display_name":null,"funder_award_id":"182565","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1707470042","https://openalex.org/W2006757043","https://openalex.org/W2023810844","https://openalex.org/W2114245236","https://openalex.org/W2155739140","https://openalex.org/W2325412727","https://openalex.org/W2585552581","https://openalex.org/W2593798028","https://openalex.org/W2748930849","https://openalex.org/W2757354308","https://openalex.org/W2787862527","https://openalex.org/W2962849048","https://openalex.org/W2962998285","https://openalex.org/W2963551825","https://openalex.org/W2963688169","https://openalex.org/W2963784458","https://openalex.org/W2963946139","https://openalex.org/W3188897366"],"related_works":["https://openalex.org/W2967700777","https://openalex.org/W2963575602","https://openalex.org/W2954725807","https://openalex.org/W3206060851","https://openalex.org/W3094114192","https://openalex.org/W2953349941","https://openalex.org/W1930217629","https://openalex.org/W2159654705","https://openalex.org/W2950861547","https://openalex.org/W3011778034","https://openalex.org/W3086487105","https://openalex.org/W2045179960","https://openalex.org/W1977186028","https://openalex.org/W3127046487","https://openalex.org/W2028821495","https://openalex.org/W2767426707","https://openalex.org/W2950080175","https://openalex.org/W3089897395","https://openalex.org/W2615167927","https://openalex.org/W2963958476"],"abstract_inverted_index":{"In":[0],"this":[1,39],"work":[2],"we":[3,54,103],"investigate":[4],"some":[5,50],"regularization":[6,111],"properties":[7],"of":[8,14],"the":[9,15,20,43,60,66,77,87,92,121],"incompressible":[10,93],"Euler":[11,78,94],"equations":[12,18,79],"and":[13,65,102,112],"fractional":[16],"Navier--Stokes":[17],"where":[19],"dissipative":[21],"term":[22],"is":[23],"given":[24],"by":[25],"$(-\\Delta)^\\alpha$":[26],"for":[27,38,49,76,91],"a":[28,110,113,117],"suitable":[29],"power":[30],"$\\alpha":[31],"\\in":[32,46,52,58,70],"(0,\\frac{1}{2})$":[33],"(the":[34],"only":[35],"meaningful":[36],"range":[37],"result).":[40],"Assuming":[41],"that":[42,56,105],"solution":[44],"$u":[45,57],"L^\\infty":[47],"_t(C^\\theta_x)$":[48],"$\\theta":[51],"(0,1)$":[53],"prove":[55],"C^\\theta_{t,x}$,":[59],"pressure":[61],"$p\\in":[62],"C^{2\\theta-}_{t,x}\\cap":[63],"C^0_t(C^{2\\theta}_x)$,":[64],"kinetic":[67],"energy":[68],"$e":[69],"C^{\\frac{2\\theta}{1-\\theta}}_t$.":[71],"This":[72],"result":[73],"was":[74],"obtained":[75],"in":[80,84],"[P.":[81],"Isett,":[82],"Regularity":[83],"time":[85],"along":[86],"coarse":[88],"scale":[89],"flow":[90],"equations,":[95],"\u016dlhttps://arXiv.org/abs/1307.0565,":[96],"2013]":[97],"with":[98],"completely":[99],"different":[100],"arguments":[101],"believe":[104],"our":[106],"proof,":[107],"based":[108],"on":[109],"commutator":[114],"estimate,":[115],"gives":[116],"simpler":[118],"insight":[119],"into":[120],"result.":[122]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}