Volume 39_1_(2018)_29-78

Long time evolution of fluids with concentrated vorticity and convergence to the point-vortex model.
Daniele Cetrone - Gabriele Serafini

Abstract. In this paper we study the evolution of vorticity in Navier-Stokes planar equations (with a small viscosity) and in Euler's axisymmetric tridimensional equations (with a large distance from the axis), when the initial vorticity is sharply concentrated around N points. We show that, in both cases, this evolution is close to the point-vortex dynamics for long times.

Rend. Mat. Appl. (7) 39 (2018) 29-78;  pdf