{"id":"https://openalex.org/W4393941667","doi":"https://doi.org/10.48550/arxiv.2404.02008","title":"Singularity formation of vortex sheets in 2D Euler equations using the\n characteristic mapping method","display_name":"Singularity formation of vortex sheets in 2D Euler equations using the\n characteristic mapping method","publication_year":2024,"publication_date":"2024-04-02","ids":{"openalex":"https://openalex.org/W4393941667","doi":"https://doi.org/10.48550/arxiv.2404.02008"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2404.02008","pdf_url":"https://arxiv.org/pdf/2404.02008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2404.02008","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000566157","display_name":"Julius Bergmann","orcid":"https://orcid.org/0009-0002-8054-9791"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bergmann, Julius","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090355873","display_name":"Thibault Maurel\u2013Oujia","orcid":"https://orcid.org/0000-0002-2806-7157"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maurel-Oujia, Thibault","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057002040","display_name":"Xiyuan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xi-Yuan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100688995","display_name":"Yin Yin","orcid":"https://orcid.org/0009-0004-0752-3039"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059988433","display_name":"Jean\u2010Christophe Nave","orcid":"https://orcid.org/0000-0003-1613-4380"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nave, Jean-Christophe","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057578130","display_name":"Kai Schneider","orcid":"https://orcid.org/0000-0003-1243-6621"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schneider, Kai","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":84},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9362,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9362,"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"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.931,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9287,"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":[],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.79559344},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.6846329},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.63968617},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.58534306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49887538},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4784841},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3489573},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.20240903}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2404.02008","pdf_url":"https://arxiv.org/pdf/2404.02008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2404.02008","pdf_url":"https://arxiv.org/pdf/2404.02008","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W3124634719","https://openalex.org/W3110381201","https://openalex.org/W2948807893","https://openalex.org/W2778153218","https://openalex.org/W2563697776","https://openalex.org/W2388608635","https://openalex.org/W1531601525","https://openalex.org/W1498128986"],"abstract_inverted_index":{"The":[0,64,151,161],"goal":[1],"of":[2,13,34,67,107,125,133,142,148,153,164,179,182,194],"this":[3,29],"numerical":[4],"study":[5],"is":[6,128,168,197],"to":[7],"get":[8],"insight":[9],"into":[10,74],"singular":[11],"solutions":[12,181],"the":[14,45,54,58,68,84,95,122,131,134,140,154,165,171,177,192,202],"two-dimensional":[15],"(2D)":[16],"Euler":[17,40,184],"equations":[18],"for":[19,25,185],"non-smooth":[20,186],"initial":[21,187],"data,":[22],"in":[23,37,101,118,170,201],"particular":[24],"vortex":[26,35,126,155,166],"sheets.":[27],"To":[28],"end":[30],"high":[31],"resolution":[32,100],"computations":[33],"layers":[36,127],"2D":[38,183],"incompressible":[39],"flows":[41],"are":[42,189],"performed":[43],"using":[44,57],"characteristic":[46],"mapping":[47],"method":[48,52,62],"(CMM).":[49],"This":[50],"semi-Lagrangian":[51],"evolves":[53],"flow":[55,69,96,113,195],"map":[56,70,97],"gradient-augmented":[59],"level":[60],"set":[61],"(GALS).":[63],"semi-group":[65],"structure":[66,163],"allows":[71],"its":[72,137],"decomposition":[73],"sub-maps":[75],"(each":[76],"over":[77],"a":[78,104,158],"finite":[79],"time":[80],"interval),":[81],"and":[82,109,144,191],"thus":[83,110],"precision":[85],"can":[86,115],"be":[87,116],"controlled":[88],"by":[89],"choosing":[90],"appropriate":[91],"remapping":[92],"times.":[93],"Composing":[94],"yields":[98],"exponential":[99],"linear":[102],"time,":[103],"unique":[105],"feature":[106],"CMM,":[108],"fine":[111],"scale":[112],"structures":[114],"resolved":[117],"great":[119],"detail.":[120],"Here":[121],"roll-up":[123],"process":[124],"studied":[129],"varying":[130],"thickness":[132,173],"layer":[135],"showing":[136],"impact":[138],"on":[139,176],"growth":[141],"palinstrophy":[143],"possible":[145],"blow":[146],"up":[147],"absolute":[149],"vorticity.":[150],"curvature":[152],"sheet":[156],"shows":[157],"singular-like":[159],"behavior.":[160],"self-similar":[162],"core":[167],"investigated":[169],"vanishing":[172],"limit.":[174],"Conclusions":[175],"non-uniqueness":[178],"weak":[180],"data":[188],"drawn":[190],"presence":[193],"singularities":[196],"revealed":[198],"tracking":[199],"them":[200],"complex":[203],"plane.":[204]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4393941667","counts_by_year":[],"updated_date":"2024-12-14T09:58:02.382668","created_date":"2024-04-05"}