A rigidity result for the Euler equations in an annulus
| Autor: | Wang, Yuchen, Zhan, Weicheng |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:2306.00302 |
| Databáze: | arXiv |
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