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

Woohyu Jeon

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arXiv · 2311.16736

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

Woohyu Jeon

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Abstract

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.

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Woohyu Jeon. 2023-11-28. A solution of 2D incompressible Euler equation with algebraic spiral roll-up in the presence of Wiener type perturbation. https://arxiv.org/abs/2311.16736

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