On the dynamics of vortices in viscous 2D flows

2022/03/14 by Stefano Ceci, Ceci, Stefano, Christian Seis +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Classical mechanics #Dynamics (music) #Fluid Dynamics and Turbulent Flows #Geometry #Integrable system #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Plane (geometry) #Point (geometry) #Thermodynamics #Viscosity #Viscous liquid #Vortex #Vorticity #Vorticity equation #Work (physics) #math.AP

paper · pdf · doi:10.48550/arxiv.2203.07185

published in arXiv (Cornell University) (Cornell University) · Improved version

openalex publication_date 2022/03/14 · arxiv created 2022/09/08 · arxiv updated 2022/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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