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An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations

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arxiv 2410.18220 v1 pith:7AAFSIHA submitted 2024-10-23 math.AP

Juan Dávila , Manuel del Pino , Monica Musso , Shrish Parmeshwar This is my paper · ORCID
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abstract

This paper addresses the long-time dynamics of solutions to the 2D incompressible Euler equations. We construct solutions with continuous vorticity $\omega_{\varepsilon}(x,t)$ concentrated around points $\xi_{j}(t)$ that converge to a sum of Dirac delta masses as $\varepsilon\to0$. These solutions are associated with the Kirchhoff-Routh point-vortex system, and the points $\xi_{j}(t)$ follow an expanding self similar trajectory of spirals, with the support of the vorticities contained in balls of radius $3\varepsilon$ around each $\xi_{j}$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Desingularization of vortex sheets for the 2D Euler equations

    math.AP 2025-05 accept novelty 8.0 of 10

    Smooth compactly supported vortex layers around any closed analytic curve evolve, in the zero-thickness limit, according to the Birkhoff-Rott equations.

  2. Stability of oppositely-propagating pair of Hill's spherical vortices

    math.AP 2025-07 conditional novelty 6.0 of 10

    An odd-symmetric pair of Hill's spherical vortices is globally stable in 3D axisymmetric Euler flow, with propagation speed close to the single-vortex speed and a sharp linear error estimate.

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