Asymptotic behavior of vortices in axisymmetric flow without swirl

摘要

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 (C) 2008 John Wiley & Sons, Ltd.