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

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.

Keywords

• Incompressible Euler flow with axisymmetry
• incompressible viscous fluid
• point vortex model
• long time behaviour