  Extending the results of Elling \cite{Elling-2013, Elling-2016}, we construct
a weak solution of 2D incompressible Euler equation with initial vorticity of
the form $w_0(x)={\left\vert x \right\vert}^{-1/\mu}g(\theta)$, where $g \in
L^p(\mathbb{T})$ satisfies $\sum_{\mathbb{Z}}{\left\vert n \right\vert}^{-0.5}
{\left\vert\widehat{g}(n)\right\vert} < \infty$. In particular, the solution is
self-similar and shows algebraic spiral roll-up.
