Multi-Sink Solutions to the Self-Similar Euler Equations

Hyungjun Choi; Matei P. Coiculescu

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arXiv · 2602.15152

Multi-Sink Solutions to the Self-Similar Euler Equations

Hyungjun Choi·Matei P. Coiculescu

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Abstract

We construct examples and provide a classification of self-similar solutions to the two-dimensional incompressible Euler equations whose pseudo-velocity fields possess more than one stagnation point. These solutions are also homogeneous steady states of the Euler equations. In contrast, we prove that any homogeneous self-similar solution with bounded vorticity away from the origin necessarily admits only a single stagnation point, located at the origin. The solutions we construct develop velocity cusps along rays from the origin, and this allows for additional stagnation points of the pseudo-velocity field.

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Hyungjun Choi, Matei P. Coiculescu. 2026-02-16. Multi-Sink Solutions to the Self-Similar Euler Equations. https://arxiv.org/abs/2602.15152

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