{"id":"https://openalex.org/W7203677087","doi":"https://doi.org/10.48550/arxiv.2608.16755","title":"Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows","display_name":"Gradient growth and relaxation to jump profiles for 3-fold symmetric scale-invariant Euler flows","publication_year":2026,"publication_date":"2026-08-17","ids":{"openalex":"https://openalex.org/W7203677087","doi":"https://doi.org/10.48550/arxiv.2608.16755"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.16755","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16755","pdf_url":"https://arxiv.org/pdf/2608.16755","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/2608.16755","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134276028","display_name":"Daomin Cao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cao, Daomin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134300743","display_name":"Junhong Fan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Junhong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012209262","display_name":"Guolin Qin","orcid":"https://orcid.org/0000-0003-1870-3970","observed_orcids":["https://orcid.org/0000-0003-1870-3970"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qin, Guolin","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":1,"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":0.9932000041007996,"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":0.9932000041007996,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.00139999995008111,"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":0.0012000000569969416,"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/two-dimensional-euler-equations","display_name":"two-dimensional Euler equations","score":0.8199999928474426},{"id":"https://openalex.org/keywords/3-fold-symmetry","display_name":"3-fold symmetry","score":0.8809999823570251},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.7599999904632568},{"id":"https://openalex.org/keywords/relaxation-theory","display_name":"relaxation theory","score":0.7120000123977661},{"id":"https://openalex.org/keywords/vorticity","display_name":"vorticity","score":0.4300000071525574}],"concepts":[{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6554999947547913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6104999780654907},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5866000056266785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5809000134468079},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5778999924659729},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32600000500679016},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.3052999973297119},{"id":"https://openalex.org/C98156149","wikidata":"https://www.wikidata.org/wiki/Q2414143","display_name":"Pressure gradient","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C137109543","wikidata":"https://www.wikidata.org/wiki/Q554388","display_name":"Temperature gradient","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.16755","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16755","pdf_url":"https://arxiv.org/pdf/2608.16755","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.2608.16755","doi":"https://doi.org/10.48550/arxiv.2608.16755","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.16755","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:2608.16755","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.16755","pdf_url":"https://arxiv.org/pdf/2608.16755","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203677087.pdf","grobid_xml":"https://content.openalex.org/works/W7203677087.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1970134625","https://openalex.org/W1980852542","https://openalex.org/W2001192987","https://openalex.org/W2014479906","https://openalex.org/W2036028870","https://openalex.org/W2046577327","https://openalex.org/W2050908105","https://openalex.org/W2055224360","https://openalex.org/W2060227954","https://openalex.org/W2060637590","https://openalex.org/W2079569943","https://openalex.org/W2086473339","https://openalex.org/W2087742667","https://openalex.org/W2118275462","https://openalex.org/W2963123674","https://openalex.org/W2963922594","https://openalex.org/W2964035818","https://openalex.org/W2971763472","https://openalex.org/W3006952923","https://openalex.org/W3121363350","https://openalex.org/W3189399604","https://openalex.org/W4224093773","https://openalex.org/W4235840289","https://openalex.org/W4320351801","https://openalex.org/W4365133282","https://openalex.org/W4365452061","https://openalex.org/W4384786022","https://openalex.org/W4388687708","https://openalex.org/W4390524154","https://openalex.org/W4390897628","https://openalex.org/W4392023130","https://openalex.org/W4392125841","https://openalex.org/W4396540949","https://openalex.org/W4400126973","https://openalex.org/W4400350435","https://openalex.org/W4401947552","https://openalex.org/W4414633228","https://openalex.org/W4417438323","https://openalex.org/W7136679804","https://openalex.org/W7140078344","https://openalex.org/W7155158063","https://openalex.org/W7163035048"],"related_works":["https://openalex.org/W4365133282","https://openalex.org/W7096582363","https://openalex.org/W1536560301","https://openalex.org/W7162198127","https://openalex.org/W7096953816","https://openalex.org/W2512605814","https://openalex.org/W2952973015","https://openalex.org/W2042036018","https://openalex.org/W2784424873","https://openalex.org/W2036028870"],"abstract_inverted_index":{"We":[0,47],"consider":[1],"long-time":[2],"behavior":[3],"of":[4,25],"the":[5,12,18,22],"zero-homogeneous":[6],"solutions":[7,44],"with":[8,45],"3-fold":[9],"symmetry":[10,43],"to":[11],"two-dimensional":[13],"Euler":[14],"equation.":[15],"This":[16],"is":[17],"remaining":[19],"case":[20],"in":[21],"relaxation":[23],"theory":[24],"Said,":[26],"Elgindi,":[27],"and":[28],"Murray":[29],"[Ann.":[30],"Sci.":[31],"\u00c9c.":[32],"Norm.":[33],"Sup\u00e9r.":[34],"(4)":[35],"\\textbf{58}":[36],"(2025),":[37],"no.~4,":[38],"943--970],":[39],"which":[40],"treats":[41],"$m$-fold":[42],"$m\\geq4$.":[46],"prove":[48],"that":[49],"every":[50],"nonconstant":[51],"$W^{1,p}$":[52],"solution":[53],"satisfies":[54],"$\\|g_\u03b8(t)\\|_{L^p}\\to\\infty$":[55],"as":[56],"$t\\to\\pm\\infty$":[57],"for":[58],"$1":[59]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-19T00:00:00"}