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Long time evolution of fluids with concentrated vorticity and convergence to the point-vortex model. (English) Zbl 1414.76014

Summary: 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.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
76D17 Viscous vortex flows
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
35Q31 Euler equations
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