Collisions and regularization for the 3-vortex problem

2004/12/09 by Antonio Hernández-Garduño, Hernández-Garduño, Antonio, Ernesto A. Lacomba +1 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements #Navier-Stokes equation solutions #math-ph #math.MP #msc:37J99 #msc:76B47

paper · pdf · doi:10.48550/arxiv.math-ph/0412024

14 pages

arxiv created 2004/12/09 · arxiv updated 2009/12/01

Abstract

We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler's equations, concentrating on the case when the moment of inertia is zero. We prove that the only motions that lead to total collisions are self-similar and that there are no binary collisions. Also, we give a regularization of the reduced system around collinear configurations (excluding binary collisions) which smoothes out the dynamics.

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