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An Expanding Self-Similar Vortex Configuration for the 2D Euler Equations https://arxiv.org/abs/2410.18220 #mathAP

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

This paper addresses the long-time dynamics of solutions to the 2D incompressible Euler equations. We construct solutions with continuous vorticity $ω_{\varepsilon}(x,t)$ concentrated around points $ξ_{j}(t)$ 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 $ξ_{j}(t)$ follow an expanding self similar trajectory of spirals, with the support of the vorticities contained in balls of radius $3\varepsilon$ around each $ξ_{j}$.

arXiv.org
October 26, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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