{"id":"https://openalex.org/W7204944090","doi":"https://doi.org/10.48550/arxiv.2608.29534","title":"Remarks on the two-dimensional Cahn-Hilliard equation forced by divergence of space-time white noise","display_name":"Remarks on the two-dimensional Cahn-Hilliard equation forced by divergence of space-time white noise","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204944090","doi":"https://doi.org/10.48550/arxiv.2608.29534"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29534","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29534","pdf_url":"https://arxiv.org/pdf/2608.29534","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/2608.29534","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148912666","display_name":"Kazuo Yamazaki","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yamazaki, Kazuo","raw_affiliation_strings":["Department of Mathematics , University of Nebraska , Lincoln , 243 Avery Hall , PO Box 880130 , Lincoln , NE 68588-0130 , U.S.A.;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Nebraska , Lincoln , 243 Avery Hall , PO Box 880130 , Lincoln , NE 68588-0130 , U.S.A.;","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5148912666"],"corresponding_institution_ids":["https://openalex.org/I114395901"],"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.35350000858306885,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.35350000858306885,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.20430000126361847,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.07989999651908875,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cahn-hilliard-equation","display_name":"Cahn-Hilliard equation","score":0.9800000190734863},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equations","display_name":"stochastic partial differential equations","score":0.8629999756813049},{"id":"https://openalex.org/keywords/space-time-white-noise","display_name":"space-time white noise","score":0.8669999837875366},{"id":"https://openalex.org/keywords/kawasaki-dynamics","display_name":"Kawasaki dynamics","score":0.8190000057220459},{"id":"https://openalex.org/keywords/renormalization","display_name":"renormalization","score":0.9380000233650208},{"id":"https://openalex.org/keywords/global-existence-and-uniqueness","display_name":"global existence and uniqueness","score":0.6660000085830688},{"id":"https://openalex.org/keywords/local-existence","display_name":"local existence","score":0.5820000171661377},{"id":"https://openalex.org/keywords/mild-solutions","display_name":"mild solutions","score":0.8859999775886536},{"id":"https://openalex.org/keywords/weak-formulation","display_name":"variational formulation","score":0.7590000033378601},{"id":"https://openalex.org/keywords/surface-quasi-geostrophic-equation","display_name":"surface quasi-geostrophic equation","score":0.8090000152587891},{"id":"https://openalex.org/keywords/two-dimensional","display_name":"two-dimensional","score":0.6539999842643738}],"concepts":[{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.7667999863624573},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.7089999914169312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.678600013256073},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5421000123023987},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5284000039100647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46320000290870667},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45989999175071716},{"id":"https://openalex.org/C166124518","wikidata":"https://www.wikidata.org/wiki/Q1047702","display_name":"Renormalization","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33059999346733093},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2587999999523163}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29534","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29534","pdf_url":"https://arxiv.org/pdf/2608.29534","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.2608.29534","doi":"https://doi.org/10.48550/arxiv.2608.29534","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29534","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:2608.29534","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29534","pdf_url":"https://arxiv.org/pdf/2608.29534","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":[{"id":"https://openalex.org/G6263472788","display_name":"EPSCoR Research Fellows: NSF: Analysis on Models of Fluid Mechanics and Mathematical Physics","funder_award_id":"2531744","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204944090.pdf","grobid_xml":"https://content.openalex.org/works/W7204944090.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1976694225","https://openalex.org/W2257908502","https://openalex.org/W2737094147","https://openalex.org/W2940176408","https://openalex.org/W4287979659","https://openalex.org/W4396618347","https://openalex.org/W4401202717","https://openalex.org/W4415081555","https://openalex.org/W4416257828","https://openalex.org/W7077878875","https://openalex.org/W7124420407","https://openalex.org/W7126077190","https://openalex.org/W7131635370","https://openalex.org/W7172416430"],"related_works":["https://openalex.org/W2111404165","https://openalex.org/W2787335972","https://openalex.org/W2241801737","https://openalex.org/W6997305430","https://openalex.org/W7207841066","https://openalex.org/W2955593534","https://openalex.org/W2121505710","https://openalex.org/W1888259362","https://openalex.org/W3036110987","https://openalex.org/W4401202717"],"abstract_inverted_index":{"We":[0,48,106],"consider":[1],"the":[2,26,33,36,50,61,75,97,101,109,135,140,163,173,179],"two-dimensional":[3],"Cahn-Hilliard":[4],"equation":[5,46,63,142,181],"forced":[6],"by":[7],"divergence":[8],"of":[9,74,87,89,96,100,114,170],"space-time":[10],"white":[11],"noise":[12],"that":[13,25,119],"represents":[14],"Kawasaki":[15],"dynamics":[16],"in":[17,66,143,187],"conservative":[18],"form.":[19],"The":[20],"standard":[21,76],"heuristic":[22],"argument":[23],"shows":[24],"solution":[27,53,112,137,171],"is":[28,39,64,104],"a":[29,67,71,115,146,151],"distribution":[30],"and":[31,93],"thus":[32],"product":[34],"within":[35],"nonlinear":[37],"term":[38],"ill-defined,":[40],"making":[41],"this":[42],"stochastic":[43],"partial":[44],"differential":[45],"challenging.":[47],"prove":[49,108,134,162],"global-in-time":[51,136,164],"unique":[52,98,111],"theory":[54,113,138],"after":[55,182],"multiple":[56,183],"Da":[57,184],"Prato-Debussche":[58,185],"tricks":[59,186],"where":[60],"last":[62,141],"solved":[65],"weak":[68,147,188],"formulation.":[69,153,189],"Besides":[70],"minimum":[72],"amount":[73],"renormalization":[77],"procedure":[78],"to":[79,130,133,161,172],"deal":[80],"with":[81,139,178],"ill-defined":[82],"products,":[83],"our":[84,120,155],"proof":[85],"consists":[86],"applications":[88],"deterministic":[90],"analysis":[91],"tools":[92],"taking":[94],"advantage":[95],"structure":[99],"equation,":[102],"which":[103],"crucial.":[105],"also":[107,150],"local-in-time":[110],"mild":[116,152],"solution,":[117],"demonstrating":[118],"improved":[121],"estimate":[122],"gets":[123],"us":[124],"arbitrarily":[125],"close,":[126],"although":[127,166],"not":[128,144,167],"quite,":[129],"being":[131],"able":[132],"only":[145],"formulation":[148],"but":[149],"Additionally,":[154],"approach":[156],"can":[157],"be":[158],"readily":[159],"extended":[160],"existence,":[165],"path-wise":[168],"uniqueness,":[169],"singular":[174],"surface":[175],"quasi-geostrophic":[176],"equations":[177],"resulting":[180]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-02T00:00:00"}
