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arXiv · 2512.18700

Rigidity for homogeneous solutions to the two-dimensional Euler equations in sector-type domains

Li Li·Xukai Yan·Zhibo Yang
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Abstract

We study the rigidity problem for $(-\alpha)$-homogeneous solutions to the two-dimensional incompressible stationary Euler equations in sector-type domains $\Omega_{a, b, \theta_0}:= \{(r,\theta): a 0$, and $b = +\infty$ or $b < +\infty$, we show that if a solution satisfies some homogeneity assumptions on the boundary of $\Omega_{a, b, \theta_0}$ and if the radial or angular component of the velocity does not vanish in $\overline{\Omega_{a, b, \theta_0}}\setminus\{\bm{0}\}$, then it must be homogeneous throughout $\overline{\Omega_{a, b, \theta_0}}\setminus\{\bm{0}\}$.

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Li Li, Xukai Yan, Zhibo Yang. 2025-12-21. Rigidity for homogeneous solutions to the two-dimensional Euler equations in sector-type domains. https://arxiv.org/abs/2512.18700

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