Vortex rings in R-3 and rearrangements

T V Badiani, G R Burton

Research output: Contribution to journalArticlepeer-review

10 Citations (SciVal)


We 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.
Original languageEnglish
Pages (from-to)1115-1135
Number of pages21
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Issue number2009
Publication statusPublished - 2001


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