From point vortices to vortex patches in self-similar expanding\n configurations

2019/12/23 by Samuel Zbarsky, Zbarsky, Samuel · 1 citation
Engineering · Mathematics · #35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1912.10862

openalex publication_date 2019/12/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The main result is that given a generic self-similarly expanding\nconfiguration of 3 point vortices that start sufficiently far out, we can\ninstead take compactly supported vorticity functions, and the resulting\nsolution to 2D incompressible Euler will evolve like a nearby point vortex\nconfiguration for all time, with the size of the patches growing at most as\nt^1/4+\ε and the distance between them growing as \√(t).\n

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• Stability of oppositely-propagating pair of Hill's spherical vortices

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