{"id":"https://openalex.org/W2145775557","doi":"https://doi.org/10.1137/110824371","title":"Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors","display_name":"Rigorous Derivation of the Thin Film Approximation with Roughness-Induced Correctors","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2145775557","doi":"https://doi.org/10.1137/110824371","mag":"2145775557"},"language":"en","primary_location":{"id":"doi:10.1137/110824371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110824371","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00565085","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048482854","display_name":"Laurent Chupin","orcid":"https://orcid.org/0000-0002-4221-0095"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurent Chupin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068312856","display_name":"S\u00e9bastien Martin","orcid":"https://orcid.org/0000-0002-6720-3051"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S\u00e9bastien Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5381,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.82596349,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"44","issue":"4","first_page":"3041","last_page":"3070"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.680400013923645,"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"}},"topics":[{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.680400013923645,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.15729999542236328,"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"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.021299999207258224,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.6716867685317993},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.6322934627532959},{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.5618459582328796},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5347933173179626},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5061718821525574},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.4929656982421875},{"id":"https://openalex.org/keywords/surface-finish","display_name":"Surface finish","score":0.4868583083152771},{"id":"https://openalex.org/keywords/stokes-flow","display_name":"Stokes flow","score":0.47884202003479004},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.4479394555091858},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.44027653336524963},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42879462242126465},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37462112307548523},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2925560176372528},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24291330575942993},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.08894440531730652},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.07998552918434143}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6716867685317993},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.6322934627532959},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.5618459582328796},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5347933173179626},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5061718821525574},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.4929656982421875},{"id":"https://openalex.org/C71039073","wikidata":"https://www.wikidata.org/wiki/Q3439090","display_name":"Surface finish","level":2,"score":0.4868583083152771},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.47884202003479004},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4479394555091858},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.44027653336524963},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42879462242126465},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37462112307548523},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2925560176372528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24291330575942993},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.08894440531730652},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.07998552918434143},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110824371","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110824371","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:CiteSeerX.psu:10.1.1.593.135","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.593.135","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/71/76/44/PDF/Chupin_Martin_Preprint2.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00565085v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00565085","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2011","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00565085v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00565085","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2011","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1443873450","display_name":"Analyse et Calcul des Effets de Rugosit\u00e9 sur les Ecoulements","funder_award_id":"ANR-08-JCJC-0104","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1981748309","https://openalex.org/W1982224354","https://openalex.org/W1992274274","https://openalex.org/W2015368175","https://openalex.org/W2018613399","https://openalex.org/W2021871259","https://openalex.org/W2025398933","https://openalex.org/W2048438132","https://openalex.org/W2053522115","https://openalex.org/W2054167585","https://openalex.org/W2059460892","https://openalex.org/W2061135763","https://openalex.org/W2064856194","https://openalex.org/W2090160848","https://openalex.org/W2109928677","https://openalex.org/W2563760622","https://openalex.org/W3104308678","https://openalex.org/W3106372520"],"related_works":["https://openalex.org/W2092584480","https://openalex.org/W2387203662","https://openalex.org/W2378338549","https://openalex.org/W4327639758","https://openalex.org/W150609566","https://openalex.org/W2360430533","https://openalex.org/W2604664877","https://openalex.org/W1998082046","https://openalex.org/W2011339542","https://openalex.org/W2154304710"],"abstract_inverted_index":{"We":[0],"derive":[1],"the":[2,12,33,37,50,59,62,82,97,104,114,119,122,128,131,134,140,151,155,159],"thin":[3],"film":[4],"approximation":[5],"including":[6],"roughness-induced":[7],"correctors.":[8],"This":[9],"corresponds":[10],"to":[11,46,58,150],"description":[13,60],"of":[14,22,36,49,61,71,81,96,116,127,133,146,158],"a":[15,47,69,143],"confined":[16,160],"Stokes":[17],"flow":[18,129],"whose":[19],"thickness":[20],"is":[21,65,163],"order":[23,43,95,147],"$\\varepsilon":[24],"\\ll":[25],"1$,":[26],"but":[27],"we":[28,101],"also":[29],"take":[30],"into":[31],"account":[32],"roughness":[34,152],"patterns":[35],"boundary":[38,76],"that":[39,103],"are":[40,91],"described":[41],"at":[42,93],"$\\varepsilon^2$,":[44],"leading":[45,57],"perturbation":[48,132],"classical":[51],"Reynolds":[52],"approximation.":[53],"The":[54,79],"asymptotic":[55],"expansion":[56],"scale":[63,124,136,145],"effects":[64,109],"rigorously":[66],"derived":[67],"through":[68],"sequence":[70],"Reynolds-type":[72],"problems":[73,84],"and":[74,85,106,130,171],"Stokes-type":[75],"layer":[77],"problems.":[78],"well-posedness":[80],"related":[83,149],"estimates":[86],"in":[87,165],"suitable":[88],"functional":[89],"spaces":[90],"proven":[92],"any":[94],"expansion.":[98],"In":[99],"particular,":[100],"show":[102],"micro-":[105,170],"macro-scale":[107,172],"coupling":[108,173],"may":[110],"be":[111],"analyzed":[112],"as":[113],"consequence":[115],"two":[117],"features:":[118],"interaction":[120,141],"between":[121],"macroscopic":[123],"(order":[125,137],"1)":[126],"microscopic":[135,144],"$\\varepsilon$)":[138],"by":[139],"with":[142],"$\\varepsilon^2$":[148],"patterns.":[153],"Moreover,":[154],"converging-diverging":[156],"profile":[157],"flow,":[161],"which":[162],"typical":[164],"lubrication":[166],"theory,":[167],"provides":[168],"additional":[169],"effects.":[174]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}