{"id":"https://openalex.org/W7204867161","doi":"https://doi.org/10.48550/arxiv.2608.28999","title":"Time periodic problem of the Navier-Stokes equations in an exterior domain with periodically moving boundary","display_name":"Time periodic problem of the Navier-Stokes equations in an exterior domain with periodically moving boundary","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204867161","doi":"https://doi.org/10.48550/arxiv.2608.28999"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28999","pdf_url":"https://arxiv.org/pdf/2608.28999","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/2608.28999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058896055","display_name":"Reinhard Farwig","orcid":"https://orcid.org/0000-0003-3068-4792","observed_orcids":["https://orcid.org/0000-0003-3068-4792"]},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Farwig, Reinhard","raw_affiliation_strings":["Fachbereich Mathematik , Technische Universit\u00e4t Darmstadt , Schlossgartenstr. 7 , 64289 Darmstadt , Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik , Technische Universit\u00e4t Darmstadt , Schlossgartenstr. 7 , 64289 Darmstadt , Germany,","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001800288","display_name":"Kazuyuki Tsuda","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I199028557","display_name":"Kyushu Sangyo University","ror":"https://ror.org/01wqrpc44","country_code":"JP","type":"education","lineage":["https://openalex.org/I199028557"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Tsuda, Kazuyuki","raw_affiliation_strings":["Kyushu Sangyo University , 3-1 Matsukadai 2-chome , Higashi-ku , Fukuoka , 813-8503 Japan ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kyushu Sangyo University , 3-1 Matsukadai 2-chome , Higashi-ku , Fukuoka , 813-8503 Japan ,","institution_ids":["https://openalex.org/I199028557"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9951000213623047,"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":0.9951000213623047,"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":0.0010000000474974513,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.0008999999845400453,"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/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.9919999837875366},{"id":"https://openalex.org/keywords/exterior-domains","display_name":"exterior domains","score":0.7760000228881836},{"id":"https://openalex.org/keywords/time-periodic-solutions","display_name":"time-periodic solutions","score":0.9369999766349792},{"id":"https://openalex.org/keywords/mild-solutions","display_name":"mild solutions","score":0.8679999709129333},{"id":"https://openalex.org/keywords/weighted-spaces","display_name":"weighted function spaces","score":0.7950000166893005},{"id":"https://openalex.org/keywords/muckenhoupt-weights","display_name":"Muckenhoupt weights","score":0.9279999732971191},{"id":"https://openalex.org/keywords/h-infinity-calculus","display_name":"H-infinity calculus","score":0.7820000052452087},{"id":"https://openalex.org/keywords/stokes-operator","display_name":"Stokes operator","score":0.8450000286102295},{"id":"https://openalex.org/keywords/weighted-lorentz-spaces","display_name":"weighted Lorentz spaces","score":0.7710000276565552},{"id":"https://openalex.org/keywords/fractional-powers","display_name":"fractional powers","score":0.4169999957084656},{"id":"https://openalex.org/keywords/potential-theory","display_name":"potential theory","score":0.3330000042915344},{"id":"https://openalex.org/keywords/homogeneous-sobolev-spaces","display_name":"homogeneous Sobolev spaces","score":0.6940000057220459},{"id":"https://openalex.org/keywords/external-forces","display_name":"external forces","score":0.44699999690055847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8133000135421753},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6718000173568726},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6477000117301941},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5260000228881836},{"id":"https://openalex.org/C2776551381","wikidata":"https://www.wikidata.org/wiki/Q6680542","display_name":"Lorentz space","level":3,"score":0.5238999724388123},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5153999924659729},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4702000021934509},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.3634999990463257},{"id":"https://openalex.org/C2779751289","wikidata":"https://www.wikidata.org/wiki/Q485292","display_name":"Analytic semigroup","level":3,"score":0.3626999855041504},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.32760000228881836},{"id":"https://openalex.org/C2456702","wikidata":"https://www.wikidata.org/wiki/Q1375954","display_name":"Vector-valued function","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C24743483","wikidata":"https://www.wikidata.org/wiki/Q1154848","display_name":"Potential theory","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.2635999917984009},{"id":"https://openalex.org/C194053038","wikidata":"https://www.wikidata.org/wiki/Q7245087","display_name":"Principal part","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C2780355006","wikidata":"https://www.wikidata.org/wiki/Q30715867","display_name":"Stokes problem","level":3,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28999","pdf_url":"https://arxiv.org/pdf/2608.28999","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.2608.28999","doi":"https://doi.org/10.48550/arxiv.2608.28999","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28999","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:2608.28999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28999","pdf_url":"https://arxiv.org/pdf/2608.28999","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/G8231511083","display_name":"\u5168\u7a7a\u9593\u4e0a\u306e\u5727\u7e2e\u6027Navier-Stokes\u65b9\u7a0b\u5f0f\u306e\u6642\u9593\u5468\u671f\u89e3\u306e\u5b89\u5b9a\u6027\u554f\u984c","funder_award_id":"22K13946","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204867161.pdf","grobid_xml":"https://content.openalex.org/works/W7204867161.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3102229831","https://openalex.org/W4403795880"],"related_works":["https://openalex.org/W4403795880","https://openalex.org/W124689772","https://openalex.org/W4404675968","https://openalex.org/W3158966132","https://openalex.org/W2898943777","https://openalex.org/W4401634529","https://openalex.org/W1976798543","https://openalex.org/W28513178","https://openalex.org/W1496964809","https://openalex.org/W2016029388"],"abstract_inverted_index":{"In":[0],"this":[1,28],"paper":[2,143],"we":[3,30],"consider":[4],"the":[5,32,92,116,126,145],"Navier-Stokes":[6],"equations":[7],"in":[8,18,42,96,110,122,153],"exterior":[9,151],"domains":[10,152,166],"of":[11,34,81,125,135],"$\\mathbb{R}^n$,":[12],"$n\\geq":[13],"3$,":[14],"with":[15,46,78],"a":[16,35,55,64,88,101,141],"periodically":[17],"time":[19,39],"moving":[20,93],"boundary":[21,94],"$\\partial\u03a9(t)$":[22],"and":[23,63,91,132],"external":[24],"force":[25],"$f(t)$.":[26],"For":[27],"case":[29],"prove":[31],"existence":[33],"locally":[36],"unique":[37],"mild":[38,70],"periodic":[40],"solution":[41,71],"weighted":[43,111,123,155],"function":[44,156],"spaces":[45,100,124],"radially":[47],"symmetric":[48],"Muckenhoupt":[49],"weights.":[50],"The":[51,147],"solutions":[52],"split":[53],"into":[54],"stationary":[56],"part":[57,67],"controlled":[58],"by":[59,144],"potential":[60],"theoretic":[61],"estimates":[62,134],"purely":[65],"oscillatory":[66],"constructed":[68],"as":[69],"via":[72],"analytic":[73],"semigroup":[74],"theory.":[75],"To":[76,114],"deal":[77],"perturbation":[79],"terms":[80],"even":[82],"second":[83],"order":[84],"-":[85,95],"coming":[86],"from":[87],"coordinate":[89],"transform":[90],"weighted,":[97],"homogeneous":[98,154],"Sobolev":[99],"maximal":[102],"$L^1$":[103],"type":[104],"regularity":[105],"estimate":[106],"will":[107],"be":[108],"used":[109],"Lorentz":[112],"spaces.":[113],"control":[115],"convective":[117],"term":[118],"an":[119],"$\\mathcal":[120],"H^\\infty$-calculus":[121,163],"Stokes":[127,148],"operator,":[128],"its":[129],"$BIP$":[130],"property":[131],"embedding":[133],"fractional":[136,165],"powers":[137],"are":[138],"exploited,":[139],"see":[140],"recent":[142],"authors:":[146],"operator":[149],"on":[150],"spaces:":[157],"From":[158],"weak":[159],"theory":[160],"to":[161,164],"$\\mathscr":[162],"(2025).":[167]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}