Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Badiani T.V. and Burton G.R 2001Vortex rings in R3 and rearrangementsProc. R. Soc. Lond. A.4571115–1135http://doi.org/10.1098/rspa.2000.0710SectionRestricted accessResearch articleVortex rings in R3 and rearrangements T.V. Badiani T.V. Badiani Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK Google Scholar Find this author on PubMed Search for more papers by this author and G.R Burton G.R Burton Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK Google Scholar Find this author on PubMed Search for more papers by this author T.V. Badiani T.V. Badiani Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK Google Scholar Find this author on PubMed Search for more papers by this author and G.R Burton G.R Burton Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 May 2001https://doi.org/10.1098/rspa.2000.0710AbstractWe study the existence of steady axisymmetric vortex rings in an ideal fluid. A functional, comprising a linear combination of kinetic energy and impulse, is to be maximized subject to the constraint that a quantity related to vorticity belongs to a set of rearrangements of a given function. Generalized solutions of a quite specific type are shown to exist, arising as extreme points of a convex extended constraint set. In the case when the given function is the indicator of a set of finite measure, the existence of proper maximizers and local maximizers is demonstrated. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Cao D, Wan J and Zhan W (2021) Desingularization of vortex rings in 3 dimensional Euler flows, Journal of Differential Equations, 10.1016/j.jde.2020.09.014, 270, (1258-1297), Online publication date: 1-Jan-2021. Rebah D (2020) Steady Vortex Rings in a Uniform Flow and Rearrangements of a Function, Results in Mathematics, 10.1007/s00025-019-1148-y, 75:1, Online publication date: 1-Mar-2020. Rebah D (2006) A steady vortex ring in Poiseuille flow and rearrangements of a function, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462:2068, (1235-1253), Online publication date: 8-Apr-2006. This Issue08 May 2001Volume 457Issue 2009 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0710Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/05/2001Published in print08/05/2001 License: Citations and impact Keywordsvortex ringsrearrangementsvariational problems