Asymmetric Self-similar Spiral Solutions of 2-D Incomressible Euler Equations

2025/07/07 by Hyungjun Choi, Choi, Hyungjun · 2 citations
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paper · pdf · doi:10.48550/arxiv.2507.05059

Abstract

We construct nonradial, self-similar solutions to the two-dimensional incompressible Euler equations without assuming rotational symmetry. These solutions extend the study of self-similar algebraic spiral flows, initiated by Elling and further developed by Shao-Wei-Zhang [41], where m-fold symmetry with m>=2 was assumed. Moreover, they bear resemblance to the numerical simulations of Bressan-Shen [10], in connection with the ongoing investigation into non-uniqueness of solutions.

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• Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data
• Homogeneous steady states for the generalized surface quasi-geostrophic equations

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