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 ${\omega }_{\epsilon }(x,t)$ concentrated around points ${\xi }_j(t)$ that converge to a sum of Dirac delta masses as $\epsilon \to 0$. 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 $3\epsilon$ around each ${\xi }_j$.