{"id":"https://openalex.org/W2007665767","doi":"https://doi.org/10.1137/080718693","title":"Numerical Study of a Flow of Regular Planar Curves That Develop Singularities at Finite Time","display_name":"Numerical Study of a Flow of Regular Planar Curves That Develop Singularities at Finite Time","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2007665767","doi":"https://doi.org/10.1137/080718693","mag":"2007665767"},"language":"en","primary_location":{"id":"doi:10.1137/080718693","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080718693","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Francisco de la Hoz","orcid":null},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco de la Hoz","raw_affiliation_strings":["University of The Basque Country"],"affiliations":[{"raw_affiliation_string":"University of The Basque Country","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I169108374"],"apc_list":null,"apc_paid":null,"fwci":0.8288,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66519293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"70","issue":"1","first_page":"279","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9879999756813049,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.7688788175582886},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.7638307809829712},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.710673987865448},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6125643253326416},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5711201429367065},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5295404195785522},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4938531517982483},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45372676849365234},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.4394811689853668},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.4229596257209778},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4170117974281311},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37777894735336304},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25432682037353516},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.08403709530830383}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.7688788175582886},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7638307809829712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.710673987865448},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6125643253326416},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5711201429367065},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5295404195785522},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4938531517982483},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45372676849365234},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.4394811689853668},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.4229596257209778},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4170117974281311},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37777894735336304},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25432682037353516},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.08403709530830383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/080718693","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080718693","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1623638918","https://openalex.org/W1997538932","https://openalex.org/W2004730271","https://openalex.org/W2011781458","https://openalex.org/W2021381560","https://openalex.org/W2027609748","https://openalex.org/W2032785697","https://openalex.org/W2065005606","https://openalex.org/W2066940865","https://openalex.org/W2077682338","https://openalex.org/W2081767934","https://openalex.org/W2102182691","https://openalex.org/W2118551292","https://openalex.org/W2134066908","https://openalex.org/W2135611868","https://openalex.org/W2144382444","https://openalex.org/W2183692121","https://openalex.org/W2468374235","https://openalex.org/W4243650062"],"related_works":["https://openalex.org/W2726339783","https://openalex.org/W2095039895","https://openalex.org/W3100214892","https://openalex.org/W2022135995","https://openalex.org/W1668363177","https://openalex.org/W4302011306","https://openalex.org/W2022448890","https://openalex.org/W2963052782","https://openalex.org/W1966148554","https://openalex.org/W2148110192"],"abstract_inverted_index":{"In":[0],"this":[1,53],"paper,":[2],"we":[3],"will":[4,71],"study":[5],"the":[6,17,24,33,38,78,86,89],"following":[7],"geometric":[8],"flow,":[9],"obtained":[10],"by":[11],"Goldstein":[12],"and":[13,36,41],"Petrich":[14],"while":[15],"considering":[16],"evolution":[18,79],"of":[19,59,80,88],"a":[20,56,64,73],"vortex":[21],"patch":[22],"in":[23,44],"plane":[25],"under":[26],"Euler's":[27],"equations:":[28],"$\\mathbf{X}_t=-k_s\\mathbf{n}-\\frac{1}{2}k^2\\mathbf{T}$,":[29],"with":[30],"s":[31],"being":[32],"arc-length":[34],"parameter":[35],"k":[37],"curvature.":[39],"Perelman":[40],"Vega":[42],"proved":[43],"[J.":[45],"Differential":[46],"Equations,":[47],"235":[48],"(2007),":[49],"pp.":[50],"56\u201373]":[51],"that":[52,62],"flow":[54],"has":[55],"one-parameter":[57],"family":[58],"regular":[60],"solutions":[61],"develop":[63],"corner-shaped":[65],"singularity":[66],"at":[67],"finite":[68],"time.":[69],"We":[70],"give":[72],"method":[74],"for":[75],"reproducing":[76],"numerically":[77],"those":[81],"solutions,":[82],"as":[83,85],"well":[84],"formation":[87],"corner,":[90],"showing":[91],"several":[92],"properties":[93],"associated":[94],"to":[95],"them.":[96]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
