A rigidity result for the Euler equations in an annulus
Analysis of PDEs
2023-06-13 v1
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.
Cite
@article{arxiv.2306.06671,
title = {A rigidity result for the Euler equations in an annulus},
author = {Yuchen Wang and Weicheng Zhan},
journal= {arXiv preprint arXiv:2306.06671},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2306.00302