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arXiv · 2410.18220

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

Juan Dávila·Manuel del Pino·Monica Musso·Shrish Parmeshwar
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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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Juan Dávila, Manuel del Pino, Monica Musso, Shrish Parmeshwar. 2024-10-23. An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations. https://arxiv.org/abs/2410.18220

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