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arXiv · 2604.09546

Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations

Averkios Averkiou·Monica Musso·Fang Yu
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Abstract

We consider the three-dimensional incompressible Euler equations for helical flows without swirl. By adapting gluing techniques, we construct the first smooth multi-vortex solution in the whole space $\mathbb{R}^3$ exhibiting a cluster of collapsing helical filaments, with the associated cross-sectional vorticity remaining compactly supported in $\mathbb{R}^2$ for all times. Our result generalises previous collapsing configurations in $\mathbb{R}^3$ with rapidly decaying vorticity cores, and extends related variational solutions obtained in infinite cylindrical domains.

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Averkios Averkiou, Monica Musso, Fang Yu. 2026-04-10. Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations. https://arxiv.org/abs/2604.09546

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