{"id":"https://openalex.org/W1981965502","doi":"https://doi.org/10.1090/s0025-5718-00-01271-0","title":"Convergence of the point vortex method for 2-D vortex sheet","display_name":"Convergence of the point vortex method for 2-D vortex sheet","publication_year":2000,"publication_date":"2000-04-13","ids":{"openalex":"https://openalex.org/W1981965502","doi":"https://doi.org/10.1090/s0025-5718-00-01271-0","mag":"1981965502"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01271-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01271-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01271-0/S0025-5718-00-01271-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01271-0/S0025-5718-00-01271-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019169169","display_name":"Jian\u2010Guo Liu","orcid":"https://orcid.org/0000-0002-9911-4045"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jian-Guo Liu","raw_affiliation_strings":["Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742"],"affiliations":[{"raw_affiliation_string":"Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101898018","display_name":"Zhouping Xin","orcid":"https://orcid.org/0000-0002-7434-2404"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Zhouping Xin","raw_affiliation_strings":["Courant Institute, New York University and IMS and Dept. of Math., The Chinese University of Hong Kong, Shatin, N.T., Hong Kong"],"affiliations":[{"raw_affiliation_string":"Courant Institute, New York University and IMS and Dept. of Math., The Chinese University of Hong Kong, Shatin, N.T., Hong Kong","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974","https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019169169"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":1.7559,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.81299238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"70","issue":"234","first_page":"595","last_page":"606"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9991000294685364,"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":0.9991000294685364,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9986000061035156,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9979000091552734,"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/vortex-sheet","display_name":"Vortex sheet","score":0.8134483098983765},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.7189388871192932},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.7172036170959473},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.696984052658081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6803843975067139},{"id":"https://openalex.org/keywords/burgers-vortex","display_name":"Burgers vortex","score":0.5795860886573792},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5663745999336243},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.5255602598190308},{"id":"https://openalex.org/keywords/vortex-stretching","display_name":"Vortex stretching","score":0.511933445930481},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.4235492944717407},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3764207363128662},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3217359185218811},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.15163540840148926}],"concepts":[{"id":"https://openalex.org/C2776672048","wikidata":"https://www.wikidata.org/wiki/Q16916679","display_name":"Vortex sheet","level":4,"score":0.8134483098983765},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.7189388871192932},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.7172036170959473},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.696984052658081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6803843975067139},{"id":"https://openalex.org/C56751440","wikidata":"https://www.wikidata.org/wiki/Q16000060","display_name":"Burgers vortex","level":4,"score":0.5795860886573792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5663745999336243},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.5255602598190308},{"id":"https://openalex.org/C91432469","wikidata":"https://www.wikidata.org/wiki/Q7941936","display_name":"Vortex stretching","level":4,"score":0.511933445930481},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.4235492944717407},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3764207363128662},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3217359185218811},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.15163540840148926}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-00-01271-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01271-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01271-0/S0025-5718-00-01271-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.7487","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.7487","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-234/S0025-5718-00-01271-0/S0025-5718-00-01271-0.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.7132","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.7132","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~jliu/research/pdf/PVM.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.20.9550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.20.9550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~jliu/research/psfiles/PVM.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01271-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01271-0","pdf_url":"https://www.ams.org/mcom/2001-70-234/S0025-5718-00-01271-0/S0025-5718-00-01271-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7699999809265137,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1131208725","display_name":"Efficient Numerical Methods for Unsteady Viscous            Incompressible Flows","funder_award_id":"9805621","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G677010205","display_name":"Mathematical Sciences:  Nonlinear Partial Differential      Equations in Continuum Mechanics","funder_award_id":"9600137","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8218179943","display_name":"Nonlinear Partial Differential Equations in Continuum Mechanics","funder_award_id":"9971978","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1981965502.pdf","grobid_xml":"https://content.openalex.org/works/W1981965502.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W6028313","https://openalex.org/W1978811720","https://openalex.org/W1987851352","https://openalex.org/W1992906507","https://openalex.org/W2001536020","https://openalex.org/W2007044713","https://openalex.org/W2022064238","https://openalex.org/W2024293593","https://openalex.org/W2034293268","https://openalex.org/W2055021661","https://openalex.org/W2068229646","https://openalex.org/W2073167527","https://openalex.org/W2074507673","https://openalex.org/W2086235031","https://openalex.org/W2093502939","https://openalex.org/W2121231927","https://openalex.org/W2133766581","https://openalex.org/W2153510147","https://openalex.org/W2164106610","https://openalex.org/W2165758297","https://openalex.org/W2169207127","https://openalex.org/W2181277443","https://openalex.org/W4234930264","https://openalex.org/W4239645461","https://openalex.org/W4241170787","https://openalex.org/W4245845296","https://openalex.org/W4247469105","https://openalex.org/W4252561870"],"related_works":["https://openalex.org/W2742629478","https://openalex.org/W2027260240","https://openalex.org/W2097362920","https://openalex.org/W2045953630","https://openalex.org/W4239677521","https://openalex.org/W4252695700","https://openalex.org/W1999573356","https://openalex.org/W2000493352","https://openalex.org/W2231760039","https://openalex.org/W1991860541"],"abstract_inverted_index":{"We":[0],"give":[1],"an":[2],"elementary":[3],"proof":[4],"of":[5,8,33,40,49],"the":[6,9,20,37,46,54,64,69,80],"convergence":[7],"point":[10,70],"vortex":[11,50,71],"method":[12,72],"(PVM)":[13],"to":[14,86],"a":[15,29,88],"classical":[16,55],"weak":[17],"solution":[18],"for":[19],"two-dimensional":[21],"incompressible":[22],"Euler":[23],"equations":[24],"with":[25],"initial":[26,38],"vorticity":[27],"being":[28],"finite":[30],"Radon":[31],"measure":[32],"distinguished":[34],"sign":[35],"and":[36],"velocity":[39,65,82],"locally":[41],"bounded":[42,76,89],"energy.":[43,92],"This":[44],"includes":[45],"important":[47],"example":[48],"sheets,":[51],"which":[52],"exhibits":[53],"Kelvin-Helmholtz":[56],"instability.":[57],"A":[58],"surprise":[59],"fact":[60],"is":[61,84],"that":[62],"although":[63],"fields":[66],"generated":[67],"by":[68],"do":[73],"not":[74],"have":[75,87],"local":[77,90],"kinetic":[78,91],"energy,":[79],"limiting":[81],"field":[83],"shown":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
