Self-Similar Solutions of the 2D Incompressible Euler Equations via a Lagrangian Construction

We give a Lagrangian construction of forward self-similar solutions of the $2$D incompressible Euler equation. For every $1<α<2$ and every real $h\in L^{2/α}(\mathbb{S}^1)$, the construction produces a flow with initial vorticity $|x|^{-α}h(\arg x)$, without smallness or sign assumptions. The argume