On the Cauchy Problem for Axi-Symmetric Vortex Rings

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Abstract

We consider the classical Cauchy problem for the three dimensional Navier–Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We show that natural approximations of the problem obtained by smoothing the initial data satisfy good uniform estimates which enable us to conclude that the original problem with the singular initial distribution of vorticity has a solution. We impose no restriction on the size of the initial data.

Original languageEnglish (US)
Pages (from-to)89-123
Number of pages35
JournalArchive For Rational Mechanics And Analysis
Volume215
Issue number1
DOIs
StatePublished - 2014

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