{"id":"https://openalex.org/W7220655724","doi":"https://doi.org/10.48550/arxiv.2610.06385","title":"Rough Axisymmetric Euler Dynamics: Global Energy Compactness and Kinetic Passage Across Regularity Breakdown","display_name":"Rough Axisymmetric Euler Dynamics: Global Energy Compactness and Kinetic Passage Across Regularity Breakdown","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220655724","doi":"https://doi.org/10.48550/arxiv.2610.06385"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06385","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06385","pdf_url":"https://arxiv.org/pdf/2610.06385","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/2610.06385","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057355659","display_name":"Gi-Chan Bae","orcid":"https://orcid.org/0000-0003-3943-3682","observed_orcids":["https://orcid.org/0000-0003-3943-3682"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bae, Gi-Chan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157779892","display_name":"Hongxu Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Hongxu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5157715288","display_name":"Chanwoo Kim","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Chanwoo","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":0.9824000000953674,"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":0.9824000000953674,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.010300000198185444,"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":0.0015999999595806003,"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/hydrodynamic-limit","display_name":"hydrodynamic limit","score":0.7160000205039978},{"id":"https://openalex.org/keywords/collisional-kinetic-equations","display_name":"collisional kinetic equations","score":0.9150000214576721},{"id":"https://openalex.org/keywords/relative-vorticity","display_name":"relative vorticity","score":0.878000020980835},{"id":"https://openalex.org/keywords/strong-solutions","display_name":"strong solutions","score":0.7960000038146973},{"id":"https://openalex.org/keywords/energy-conservation-physics","display_name":"energy conservation (physics)","score":0.43299999833106995},{"id":"https://openalex.org/keywords/rough-initial-data","display_name":"rough initial data","score":0.546999990940094}],"concepts":[{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.7739999890327454},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6916000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6894999742507935},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.6083999872207642},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5945000052452087},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5666999816894531},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5454000234603882},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.48809999227523804},{"id":"https://openalex.org/C2781217745","wikidata":"https://www.wikidata.org/wiki/Q1053779","display_name":"Euler system","level":3,"score":0.4749999940395355},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.44179999828338623},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4221999943256378},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.3790999948978424},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.296999990940094},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C196102512","wikidata":"https://www.wikidata.org/wiki/Q1340031","display_name":"Euler number (physics)","level":5,"score":0.2773999869823456},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2989268449","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Energy method","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06385","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06385","pdf_url":"https://arxiv.org/pdf/2610.06385","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.2610.06385","doi":"https://doi.org/10.48550/arxiv.2610.06385","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06385","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:2610.06385","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06385","pdf_url":"https://arxiv.org/pdf/2610.06385","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/G1640782566","display_name":"CAREER: Hilberts Sixth Problem in the Boltzmann equation","funder_award_id":"2047681","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2286686988","display_name":"SLMath: Opening Doors to Mathematics","funder_award_id":"2424139","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2368185376","display_name":null,"funder_award_id":"2021R1C1C2094843","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G4713160749","display_name":null,"funder_award_id":"2424139","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220655724.pdf","grobid_xml":"https://content.openalex.org/works/W7220655724.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4416021344","https://openalex.org/W4417459271","https://openalex.org/W7137878744","https://openalex.org/W7161236379"],"related_works":["https://openalex.org/W3003638555","https://openalex.org/W2963174542","https://openalex.org/W3193812556","https://openalex.org/W2951283021","https://openalex.org/W7095968976","https://openalex.org/W3197390197","https://openalex.org/W2952724437","https://openalex.org/W2733030916","https://openalex.org/W6927417486","https://openalex.org/W4299360475"],"abstract_inverted_index":{"We":[0,67],"establish":[1],"global":[2,163],"energy":[3],"compactness":[4],"for":[5,44,85,88],"rough":[6,112],"three-dimensional":[7],"axisymmetric":[8,120],"Euler":[9,26,37,114,121,132,146,165],"flow":[10],"without":[11,46,81],"swirl":[12],"and":[13,95,117,153],"use":[14],"it":[15],"to":[16,143,149],"construct":[17,104],"hydrodynamic":[18,140],"limits":[19,122],"of":[20,63,98],"collisional":[21],"kinetic":[22],"equations":[23],"beyond":[24],"finite-time":[25],"regularity":[27,135],"breakdown.":[28],"For":[29,90],"relative":[30],"vorticity":[31],"in":[32,42,136],"$L^1\\cap":[33],"L^p$,":[34],"regular":[35,131,145],"approximate":[36],"flows":[38],"are":[39],"globally":[40],"compact":[41],"$C_tL_x^2$":[43],"$p\\ge4/3$,":[45],"a":[47,82,96,155],"sign":[48,83],"condition":[49,84],"or":[50],"any":[51],"spatial-moment":[52],"assumption.":[53],"Below":[54],"$4/3$,":[55],"the":[56,64,69,76,91,129,139,144,150],"same":[57],"conclusion":[58],"holds":[59],"under":[60],"uniform":[61],"control":[62],"absolute":[65,77],"impulse.":[66],"identify":[68],"sharp":[70],"radial":[71],"dynamics":[72],"governing":[73],"this":[74],"confinement:":[75],"impulse":[78],"is":[79],"propagated":[80],"$p\\ge5/3$,":[86],"while":[87,160],"$11$.":[89],"Coulomb":[92],"Landau":[93],"equation":[94],"class":[97],"non-cutoff":[99],"soft-potential":[100],"Boltzmann":[101],"equations,":[102],"we":[103],"strong":[105,157],"solutions":[106],"on":[107,123],"lifespans":[108],"$T^\\varepsilon\\to\\infty$":[109],"realizing":[110],"prescribed":[111],"finite-energy":[113],"initial":[115],"data":[116],"obtain":[118],"energy-conserving":[119,164],"every":[124],"fixed":[125],"time":[126,152],"interval.":[127],"If":[128],"corresponding":[130],"evolution":[133],"loses":[134],"finite":[137],"time,":[138],"fields":[141],"converge":[142],"solution":[147],"up":[148],"singular":[151],"have":[154],"common":[156],"trace":[158],"there,":[159],"subsequences":[161],"yield":[162],"continuations":[166],"past":[167],"that":[168],"time.":[169]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}