{"id":"https://openalex.org/W7214101716","doi":"https://doi.org/10.48550/arxiv.2609.25119","title":"Critical homogenization of the Navier--Stokes--Cahn--Hilliard system in perforated domains","display_name":"Critical homogenization of the Navier--Stokes--Cahn--Hilliard system in perforated domains","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214101716","doi":"https://doi.org/10.48550/arxiv.2609.25119"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25119","pdf_url":"https://arxiv.org/pdf/2609.25119","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.25119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140670628","display_name":"Jiaojiao Pan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan, Jiaojiao","raw_affiliation_strings":["School of Mathematics , Nanjing University , Nanjing 210093 , China,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Nanjing University , Nanjing 210093 , China,","institution_ids":["https://openalex.org/I881766915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5140674534","display_name":"Luqi Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Luqi","raw_affiliation_strings":["School of Mathematics , Nanjing University , Nanjing 210093 , China,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Nanjing University , Nanjing 210093 , China,","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I881766915"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.8574000000953674,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.8574000000953674,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.09149999916553497,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.011900000274181366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/navier-stokes-cahn-hilliard-system","display_name":"Cahn-Hilliard-Navier-Stokes system","score":0.984000027179718},{"id":"https://openalex.org/keywords/perforated-domains","display_name":"perforated domains","score":0.871999979019165},{"id":"https://openalex.org/keywords/phase-field-model","display_name":"phase-field model","score":0.4000000059604645},{"id":"https://openalex.org/keywords/energy-concentration","display_name":"energy concentration","score":0.5},{"id":"https://openalex.org/keywords/cahn-hilliard-equation","display_name":"Cahn-Hilliard equation","score":0.8799999952316284},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"incompressible flow","score":0.6370000243186951},{"id":"https://openalex.org/keywords/three-dimensional-domains","display_name":"three-dimensional domains","score":0.4480000138282776}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7785999774932861},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6883000135421753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6202999949455261},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5144000053405762},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5037999749183655},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C196806460","wikidata":"https://www.wikidata.org/wiki/Q188603","display_name":"Capillary action","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3384000062942505},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.33489999175071716},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C19191322","wikidata":"https://www.wikidata.org/wiki/Q674202","display_name":"Stokes flow","level":3,"score":0.2865999937057495},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.25119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25119","pdf_url":"https://arxiv.org/pdf/2609.25119","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.25119","doi":"https://doi.org/10.48550/arxiv.2609.25119","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25119","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.25119","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25119","pdf_url":"https://arxiv.org/pdf/2609.25119","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214101716.pdf","grobid_xml":"https://content.openalex.org/works/W7214101716.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W2046127134","https://openalex.org/W2052033052","https://openalex.org/W2073078790","https://openalex.org/W2110096798","https://openalex.org/W2120248903","https://openalex.org/W2120554329","https://openalex.org/W2164402335","https://openalex.org/W2168524315","https://openalex.org/W2763765438","https://openalex.org/W3081552335","https://openalex.org/W3107875181","https://openalex.org/W3163053919","https://openalex.org/W3216064893","https://openalex.org/W4292024663","https://openalex.org/W4408147547","https://openalex.org/W4413093155","https://openalex.org/W4413424644","https://openalex.org/W7117336086","https://openalex.org/W7157876815","https://openalex.org/W7169473549"],"related_works":["https://openalex.org/W7117339471","https://openalex.org/W7169473549","https://openalex.org/W7221785697","https://openalex.org/W4408147547","https://openalex.org/W4405116239","https://openalex.org/W1986580052","https://openalex.org/W3108399206","https://openalex.org/W1964548748","https://openalex.org/W4387501292","https://openalex.org/W2908809115"],"abstract_inverted_index":{"We":[0,170],"consider":[1],"the":[2,32,40,54,67,72,80,83,87,92,107,116,120,136,159,164,179,183],"three-dimensional":[3],"incompressible":[4],"Navier--Stokes--Cahn--Hilliard":[5],"(NSCH)":[6],"system":[7,52],"in":[8,109,119,154],"domains":[9],"perforated":[10],"by":[11,20,66],"no-slip":[12],"obstacles":[13],"of":[14,16,22,71,91,106,115],"diameter":[15],"order":[17,23],"\\(\\varepsilon^3\\)":[18],"separated":[19],"distances":[21],"\\(\\varepsilon\\).":[24],"Both":[25],"viscosity":[26,85,118],"and":[27,45,86,111,148,156,163],"mobility":[28],"may":[29],"depend":[30],"on":[31],"phase":[33,46,108],"variable.":[34],"At":[35],"this":[36,130],"critical":[37,93],"Stokes-capacity":[38],"scale,":[39],"limiting":[41],"velocity":[42,181],"\\(\\boldsymbol":[43],"u\\)":[44],"field":[47],"\\(\u03d5\\)":[48],"satisfy":[49],"an":[50,186,192],"NSCH":[51],"with":[53,124],"additional":[55],"Brinkman":[56,161],"resistance":[57],"\\(\u03bd(\u03d5)\\mathbf":[58],"B\\boldsymbol":[59],"u\\),":[60],"where":[61],"\\(\\mathbf":[62],"B\\)":[63],"is":[64,79,185],"determined":[65],"exterior":[68],"Stokes":[69,94],"capacity":[70],"reference":[73],"obstacle.":[74],"The":[75,96,140],"principal":[76],"analytical":[77],"difficulty":[78],"interaction":[81],"between":[82],"phase-dependent":[84,117],"order-one":[88],"energy":[89],"concentration":[90],"correctors.":[95],"variational":[97],"chemical-potential":[98],"identity":[99],"yields,":[100],"after":[101],"scalar":[102],"extension,":[103],"strong":[104,113],"convergence":[105,114],"\\(L^2(0,T;H^1(\u03a9))\\),":[110],"hence":[112],"same":[121],"topology.":[122],"Combined":[123],"a":[125,173],"cellwise":[126],"Hardy":[127],"multiplier":[128],"estimate,":[129],"compactness":[131],"can":[132],"be":[133],"transferred":[134],"through":[135],"concentrated":[137],"corrector":[138],"layer.":[139],"resulting":[141],"weighted-capacity":[142],"statement":[143],"applies":[144],"to":[145,191],"uniformly":[146],"positive":[147],"bounded":[149],"coefficient":[150,176],"sequences":[151],"converging":[152],"strongly":[153],"\\(L^2(0,T;H^1(\u03a9))\\)":[155],"simultaneously":[157],"identifies":[158],"effective":[160],"force":[162],"corresponding":[165],"viscous":[166],"dissipation":[167],"lower":[168],"bound.":[169],"also":[171],"investigate":[172],"vanishing":[174],"capillary":[175],"\\(\u03bb_\\varepsilon\\to0\\).":[177],"After":[178],"natural":[180],"scaling,":[182],"limit":[184],"unsteady":[187],"Stokes--Brinkman":[188],"equation":[189],"coupled":[190],"unadvected":[193],"Cahn--Hilliard":[194],"equation.":[195]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}