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

A solution of 2D incompressible Euler equation with algebraic spiral roll-up in the presence of Wiener type perturbation