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Concentrated vortex rings for Euler and Navier-Stokes equations

By Guido Cavallaro

Appears in collection : Summer School 2023 - New trends in mathematical fluid dynamics

We study the time evolution of an incompressible fluid (both inviscid and viscous) with axial symmetry without swirl, when the initial vorticity is very concentrated in N disjoint rings. We show that in a suitable limit, in which the thickness of the rings (and the viscosity, in the viscous case) tends to zero, the vorticity remains concentrated in N disjointed rings, each one of them performing a simple translation along the symmetry axis with constant speed.

Information about the video

  • Date of recording 07/06/2023
  • Date of publication 09/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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