{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:47:31Z","timestamp":1776725251204,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"234","license":[{"start":{"date-parts":[[2001,4,13]],"date-time":"2001-04-13T00:00:00Z","timestamp":987120000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the two-dimensional incompressible Euler equations with initial vorticity being a finite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instability. A surprise fact is that although the velocity fields generated by the point vortex method do not have bounded local kinetic energy, the limiting velocity field is shown to have a bounded local kinetic energy.<\/p>","DOI":"10.1090\/s0025-5718-00-01271-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:17:46Z","timestamp":1027707466000},"page":"595-606","source":"Crossref","is-referenced-by-count":21,"title":["Convergence of the point vortex method for 2-D vortex sheet"],"prefix":"10.1090","volume":"70","author":[{"given":"Jian-Guo","family":"Liu","sequence":"first","affiliation":[]},{"given":"Zhouping","family":"Xin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2000,4,13]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-1-4613-9121-0_3","article-title":"The approximation of weak solutions to the 2-D Euler equations by vortex elements","author":"Beale, J. 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