  We present a symmetry result regarding stationary solutions of the 2D Euler
equations in a disk. We prove that in a disk, a steady flow with only one
stagnation point and tangential boundary conditions is a circular flow, which
confirms a conjecture proposed by F. Hamel and N. Nadirashvili in [J. Eur.
Math. Soc., 25 (2023), no. 1, 323-368]. The key ingredient of the proof is to
use `local' symmetry properties for the non-negative solutions of semi-linear
elliptic equations with a continuous nonlinearity in a ball, which can be
established by a rearrangement technique called continuous Steiner
symmetrization.
