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arXiv · 2608.13134

Uniformly Rotating Vortex Patches with 90-Degree Corners

De Huang·Jiajun Tong·Xiaopeng Zheng
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Abstract

For the 2-D incompressible Euler equation, we prove the existence of $m$-fold symmetric uniformly rotating vortex patches with 90-degree corners for all $m\geq 12$. Properties of these patches and the induced stationary flows in the co-rotating frame are characterized. Our construction is based on a novel fixed-point method.

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De Huang, Jiajun Tong, Xiaopeng Zheng. 2026-08-13. Uniformly Rotating Vortex Patches with 90-Degree Corners. https://arxiv.org/abs/2608.13134

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