Remarks on radial symmetry of stationary and uniformly-rotating solutions for the 2D Euler equation
We prove that any uniformly rotating solution of the 2D incompressible Euler equation with compactly supported vorticity $ω$ must be radially symmetric whenever its angular velocity satisfies $Ω\in (-\infty,\inf ω/ 2] \cup \, [ \sup ω/ 2, +\infty )$, in both the patch and smooth settings. This result extends the rigidity theorems established in \cite{Gom2021MR4312192} (\textit{Duke Math. J.},170(13):2957-3038, 2021), which were confined to the case of non-positive angular velocities and non…
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