On the dynamics of vortices in viscous 2D flows

2022/03/14 by Stefano Ceci, Ceci, Stefano, Christian Seis +1 · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2203.07185

Abstract

We study the 2D Navier--Stokes solution starting from an initial vorticity mildly concentrated near N distinct points in the plane. We prove quantitative estimates on the propagation of concentration near a system of interacting point vortices introduced by Helmholtz and Kirchhoff. Our work extends the previous results in the literature in three ways: The initial vorticity is concentrated in a weak (Wasserstein) sense, it is merely L^p integrable for some p>2, and the estimates we derive are uniform with respect to the viscosity.

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• Long time confinement of multiple concentrated vortices

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