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arXiv · 2306.06671

A rigidity result for the Euler equations in an annulus

Yuchen Wang·Weicheng Zhan
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Abstract

We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which addresses an open question proposed by F. Hamel and N. Nadirashvili in [J. Eur. Math. Soc., 25 (2023), no. 1, 323-368]. The proof is based on the study of the geometric properties of the streamlines of the flow and on `local' symmetry properties for the non-negative solutions of semi-linear elliptic equations with a continuous nonlinearity.

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Yuchen Wang, Weicheng Zhan. 2023-06-11. A rigidity result for the Euler equations in an annulus. https://arxiv.org/abs/2306.06671

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