{"id":"https://openalex.org/W4387060725","doi":"https://doi.org/10.1137/22m1500587","title":"The Sharp Interface Limit of a Navier\u2013Stokes/Allen\u2013Cahn System with Constant Mobility: Convergence Rates by a Relative Energy Approach","display_name":"The Sharp Interface Limit of a Navier\u2013Stokes/Allen\u2013Cahn System with Constant Mobility: Convergence Rates by a Relative Energy Approach","publication_year":2023,"publication_date":"2023-09-26","ids":{"openalex":"https://openalex.org/W4387060725","doi":"https://doi.org/10.1137/22m1500587"},"language":"en","primary_location":{"id":"doi:10.1137/22m1500587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1500587","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002584428","display_name":"Sebastian Hensel","orcid":"https://orcid.org/0000-0001-7252-8072"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4391767997","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36","country_code":null,"type":"facility","lineage":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sebastian Hensel","raw_affiliation_strings":["Hausdorff Center for Mathematics, Universit\u00e4t Bonn, 53115 Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Hausdorff Center for Mathematics, Universit\u00e4t Bonn, 53115 Bonn, Germany","institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4391767997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028609488","display_name":"Yuning Liu","orcid":"https://orcid.org/0000-0002-9903-6104"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuning Liu","raw_affiliation_strings":["NYU Shanghai, Pudong, Shanghai 200126, China, and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, 200062, China"],"affiliations":[{"raw_affiliation_string":"NYU Shanghai, Pudong, Shanghai 200126, China, and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, 200062, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002584428"],"corresponding_institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4391767997"],"apc_list":null,"apc_paid":null,"fwci":1.4119,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84443841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"55","issue":"5","first_page":"4751","last_page":"4787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9961000084877014,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9961000084877014,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9915000200271606,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6912832856178284},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6713114976882935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6271964907646179},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6243975162506104},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.558821976184845},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5353773832321167},{"id":"https://openalex.org/keywords/allen\u2013cahn-equation","display_name":"Allen\u2013Cahn equation","score":0.5300224423408508},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5073997378349304},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5049646496772766},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49264270067214966},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.47286128997802734},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4503360092639923},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4482979476451874},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.43107423186302185},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41905975341796875},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.41785621643066406},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.41281840205192566},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3000919818878174},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.25348997116088867},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18831655383110046},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09491541981697083}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6912832856178284},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6713114976882935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6271964907646179},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6243975162506104},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.558821976184845},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5353773832321167},{"id":"https://openalex.org/C2777166216","wikidata":"https://www.wikidata.org/wiki/Q4732089","display_name":"Allen\u2013Cahn equation","level":2,"score":0.5300224423408508},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5073997378349304},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5049646496772766},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49264270067214966},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.47286128997802734},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4503360092639923},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4482979476451874},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.43107423186302185},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41905975341796875},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.41785621643066406},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.41281840205192566},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3000919818878174},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.25348997116088867},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18831655383110046},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09491541981697083},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1500587","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1500587","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8100000023841858}],"awards":[{"id":"https://openalex.org/G5853897010","display_name":null,"funder_award_id":"11971314","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7135710844","display_name":null,"funder_award_id":"EXC-2047/1 - 39068581","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W35304917","https://openalex.org/W1539347723","https://openalex.org/W1550550133","https://openalex.org/W1593414945","https://openalex.org/W1986635690","https://openalex.org/W1990510363","https://openalex.org/W1998888747","https://openalex.org/W2003610831","https://openalex.org/W2010502651","https://openalex.org/W2021384657","https://openalex.org/W2030229707","https://openalex.org/W2041968314","https://openalex.org/W2047626766","https://openalex.org/W2049031884","https://openalex.org/W2058380015","https://openalex.org/W2058453180","https://openalex.org/W2066359652","https://openalex.org/W2076964660","https://openalex.org/W2086238793","https://openalex.org/W2138618054","https://openalex.org/W2149606697","https://openalex.org/W2170339701","https://openalex.org/W2171422900","https://openalex.org/W2331215403","https://openalex.org/W2567182430","https://openalex.org/W2594436551","https://openalex.org/W2761918954","https://openalex.org/W2909878604","https://openalex.org/W2962823729","https://openalex.org/W2963244207","https://openalex.org/W2963781498","https://openalex.org/W2963827895","https://openalex.org/W2963958190","https://openalex.org/W2964014713","https://openalex.org/W2976567125","https://openalex.org/W3014905701","https://openalex.org/W3092855995","https://openalex.org/W3098115558","https://openalex.org/W3099486368","https://openalex.org/W3104533527","https://openalex.org/W3112433806","https://openalex.org/W3132668627","https://openalex.org/W3137084936","https://openalex.org/W3173721653","https://openalex.org/W3188339550","https://openalex.org/W3190238824","https://openalex.org/W3215884613","https://openalex.org/W4205235980","https://openalex.org/W4289223958","https://openalex.org/W4293215819"],"related_works":["https://openalex.org/W2331268773","https://openalex.org/W2965060133","https://openalex.org/W2155362166","https://openalex.org/W1983679522","https://openalex.org/W1992107226","https://openalex.org/W2069302992","https://openalex.org/W2339294360","https://openalex.org/W2902703932","https://openalex.org/W3100688885","https://openalex.org/W1995551146"],"abstract_inverted_index":{".We":[0],"investigate":[1],"the":[2,13,17,47,50,66,80,85,93,96,104,111,114,130],"sharp":[3],"interface":[4,9,107],"limit":[5,71,97],"of":[6,49,95,113,134],"a":[7,22,38,42,56,70],"diffuse":[8],"system":[10,20,74,98],"that":[11,65,78,92,103],"couples":[12,79],"Allen\u2013Cahn":[14],"equation":[15],"with":[16,27,46,75],"instationary":[18],"Navier\u2013Stokes":[19,86],"in":[21,25,41,140],"bounded":[23],"domain":[24],"\\(\\mathbb{R}^d\\)":[26],"\\(d":[28],"\\in":[29],"\\{2,3\\}\\)":[30],".":[31,62],"This":[32,128],"model":[33],"is":[34,99,129,138],"used":[35],"to":[36,69],"describe":[37],"propagating":[39],"front":[40],"viscous":[43],"incompressible":[44],"flow":[45,83],"width":[48],"transition":[51],"layer":[52],"being":[53],"characterized":[54],"by":[55],"small":[57],"parameter":[58],"\\(\\varepsilon":[59],"\\gt":[60],"0\\)":[61],"We":[63],"show":[64],"solutions":[67],"converge":[68],"two-phase":[72],"fluid":[73],"surface":[76],"tension":[77],"mean":[81],"curvature":[82],"and":[84,102],"system.":[87],"The":[88],"main":[89],"assumptions":[90],"are":[91],"evolution":[94],"sufficiently":[100],"regular":[101],"associated":[105],"evolving":[106],"does":[108],"not":[109],"intersect":[110],"boundary":[112],"container.":[115],"For":[116],"quantitatively":[117],"well-prepared":[118],"initial":[119],"data,":[120],"we":[121],"even":[122],"establish":[123],"an":[124],"optimal":[125],"convergence":[126],"rate.":[127],"first":[131],"rigorous":[132],"result":[133],"this":[135],"kind":[136],"which":[137],"valid":[139],"all":[141],"physically":[142],"relevant":[143],"ambient":[144],"dimensions.KeywordsAllen\u2013Cahn":[145],"equationMSC":[146],"codes76T9976D4576D0535R3553E1035K57":[147]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
