Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data

Given $0<a<1$ and any $C^1$, divergence-free, $(-a)$-homogeneous vector field $u_0$ on the punctured plane, we construct a forward self-similar solution of the two-dimensional incompressible Euler equations on the plane with initial datum $u_0$. No smallness or sign condition is required. The soluti