We study the time evolution of an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks. We discuss how long this concentration persists, showing that in some cases this happens for quite long times. Moreover, we analyze a toy model that shows a similar behavior and gives some hints on the original problem
We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider N disjoint vortex rings of size ε and intensity of the order of | log ε| - 1. We show that in the limit ε→ 0 , when the density of vorticity becomes very large, the movement of each vortex ring converges to a simple translation, at least for a small but positive time.
© Università degli Studi di Roma "La Sapienza" - Piazzale Aldo Moro 5, 00185 Roma
