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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T04:34:50Z","timestamp":1692678890325},"reference-count":55,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Comm Pure Appl Math"],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in a suitable H\u00f6lder space and the vorticity may not have a distinguished sign. Our solutions are obtained by means of convex integration; they are smooth outside a \u201cturbulence\u201d zone which grows linearly in time around the vortex sheet. As a by\u2010product, this approach shows how the growth of the turbulence zone is controlled by the local energy inequality and measures the maximal initial dissipation rate in terms of the vortex sheet strength. \u00a9 2021 The Authors. <jats:italic>Communications on Pure and Applied Mathematics<\/jats:italic> published by Wiley Periodicals LLC.<\/jats:p>","DOI":"10.1002\/cpa.22038","type":"journal-article","created":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T09:03:44Z","timestamp":1642064624000},"page":"163-221","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign"],"prefix":"10.1002","volume":"76","author":[{"given":"Francisco","family":"Mengual","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad Aut\u00f3noma de Madrid Calle Francisco Tom\u00e1s y Valiente, 7 28049 Madrid Spain"}]},{"suffix":"Jr","given":"L\u00e1szl\u00f3","family":"Sz\u00e9kelyhidi","sequence":"additional","affiliation":[{"name":"Mathematisches Institut, Universit\u00e4t Leipzig Augustusplatz 10 04109 Leipzig Germany"}]}],"member":"311","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Birkhoff G.Helmholtz and Taylor instability.Proc. Sympos. Appl. Math. Vol. XIII 55\u2010\u00e2\u20ac\u201c76. American Mathematical Society Providence R.I. 1962.","DOI":"10.1090\/psapm\/013\/0137423"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00220\u2010011\u20101267\u20100"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21781"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21897"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0726059"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/0520020"},{"key":"e_1_2_1_8_1","first-page":"1605.04822 [mat","article-title":"Mixing solutions for the Muskat problem","author":"Castro A.","year":"2016","journal-title":"Preprint"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"Castro A.;C\u00f3rdoba D.;Gancedo F.A naive parametrization for the vortex\u2010sheet problem.Mathematical aspects of fluid mechanics 88\u2010\u00e2\u20ac\u201c115. London Mathematical Society Lecture Note Series 402. Cambridge Univ. Press Cambridge 2012.","DOI":"10.1017\/CBO9781139235792.006"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","unstructured":"Castro A.;Faraco D.;Mengual F.Degraded mixing solutions for the Muskat problem.Calc. Var. Partial Differential Equations58(2019) no. 2 Paper No. 58 29 pp. doi: 10.1007\/s00526\u2010019\u20101489\u20100","DOI":"10.1007\/s00526-019-1489-0"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21537"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00205\u2010014
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