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Asymptotic behavior of vortices in axisymmetric flow without swirl
Author(s) -
Ren Kun,
Tang TaiMan
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1024
Subject(s) - rotational symmetry , vortex , mathematics , symmetry (geometry) , bounded function , compressibility , flow (mathematics) , axis of symmetry , symmetry in biology , euler equations , euler's formula , geometry , mechanics , mathematical analysis , physics
We investigate the confinement properties of bounded, nonnegative, compactly supported vortices of axisymmetric incompressible Euler flows without swirl. We show that along one direction of the symmetry axis, its support can grow no faster than O [( t log t ) 1/2 ]. The rate at which it approaches the symmetry axis is also estimated. Together with the result of Maffei–Marchioro on the radial growth rate of the support, it is contained in a slowly expanding tubular region. The techniques of the above‐mentioned authors, Iftimie–Lopes–Nussenzveig and Iftimie–Sideris–Gamblin, are used. Copyright © 2008 John Wiley & Sons, Ltd.