{"id":"https://openalex.org/W7213863256","doi":"https://doi.org/10.48550/arxiv.2609.21244","title":"Lower bounds for the lifespan of solutions to the Euler--Korteweg equations","display_name":"Lower bounds for the lifespan of solutions to the Euler--Korteweg equations","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7213863256","doi":"https://doi.org/10.48550/arxiv.2609.21244"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21244","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21244","pdf_url":"https://arxiv.org/pdf/2609.21244","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/2609.21244","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152394306","display_name":"Haruhiro Kurabe","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kurabe, Haruhiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035921381","display_name":"Ryo Takada","orcid":"https://orcid.org/0000-0002-7958-5819","observed_orcids":["https://orcid.org/0000-0002-7958-5819"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Takada, Ryo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134362940","display_name":"Tomoaki Yoshizawa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yoshizawa, Tomoaki","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":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":0.7182999849319458,"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":0.7182999849319458,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.274399995803833,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00139999995008111,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lifespan-of-solutions","display_name":"lifespan of solutions","score":0.8360000252723694},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8579999804496765},{"id":"https://openalex.org/keywords/irrotational-flow","display_name":"irrotational flow","score":0.9580000042915344},{"id":"https://openalex.org/keywords/weber-number","display_name":"Weber number","score":0.7089999914169312},{"id":"https://openalex.org/keywords/mach-number","display_name":"Mach number","score":1.0},{"id":"https://openalex.org/keywords/sobolev-norms","display_name":"Sobolev norms","score":0.7720000147819519},{"id":"https://openalex.org/keywords/compressible-fluid-dynamics","display_name":"compressible fluid dynamics","score":0.5809999704360962},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"initial value problems","score":0.7639999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7692999839782715},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6355000138282776},{"id":"https://openalex.org/C147457402","wikidata":"https://www.wikidata.org/wiki/Q1588205","display_name":"Conservative vector field","level":3,"score":0.6241999864578247},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5932000279426575},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5753999948501587},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5425999760627747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5156999826431274},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C165231844","wikidata":"https://www.wikidata.org/wiki/Q160669","display_name":"Mach number","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.39410001039505005},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.37369999289512634},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.26170000433921814}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.21244","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21244","pdf_url":"https://arxiv.org/pdf/2609.21244","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.2609.21244","doi":"https://doi.org/10.48550/arxiv.2609.21244","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21244","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:2609.21244","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21244","pdf_url":"https://arxiv.org/pdf/2609.21244","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/G4230151703","display_name":"\u5206\u6563\u6027\u3092\u6709\u3059\u308b\u5727\u7e2e\u6027\u6d41\u4f53\u65b9\u7a0b\u5f0f\u306e\u6570\u7406\u89e3\u6790","funder_award_id":"26K06876","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5591695716","display_name":"\u5730\u7403\u6d41\u4f53\u304a\u3088\u3073\u78c1\u6c17\u6d41\u4f53\u65b9\u7a0b\u5f0f\u306b\u73fe\u308c\u308b\u5206\u6563\u6027\u306e\u6570\u5b66\u89e3\u6790","funder_award_id":"22K03388","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/W7213863256.pdf","grobid_xml":"https://content.openalex.org/works/W7213863256.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223006511","https://openalex.org/W4288336254","https://openalex.org/W3126686032","https://openalex.org/W4298376009","https://openalex.org/W2070066893","https://openalex.org/W1840992002","https://openalex.org/W4414787817","https://openalex.org/W4403995894","https://openalex.org/W7170033661","https://openalex.org/W2090872027"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,7,11,30,40,43,47,51,74],"initial":[3,52],"value":[4],"problem":[5],"for":[6,29],"Euler--Korteweg":[8],"equations":[9],"in":[10,64],"class":[12],"of":[13,32,50],"irrotational":[14],"flows.":[15],"In":[16,54],"every":[17],"space":[18],"dimension":[19],"$d":[20],"\\geqslant":[21],"2$,":[22],"we":[23],"establish":[24],"a":[25,65,69],"quantitative":[26],"lower":[27,57],"bound":[28,58],"lifespan":[31],"solutions":[33],"that":[34],"explicitly":[35],"exhibits":[36],"its":[37],"dependence":[38],"on":[39],"Weber":[41,77],"number,":[42,45],"Mach":[44,75],"and":[46,76],"Sobolev":[48],"norm":[49],"perturbation.":[53],"particular,":[55],"this":[56],"can":[59],"be":[60],"taken":[61],"arbitrarily":[62],"large":[63],"low-Weber-number":[66],"regime":[67],"under":[68],"suitable":[70],"algebraic":[71],"relation":[72],"between":[73],"numbers.":[78]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-22T00:00:00"}