Every uniformly rotating vortex patch in the unit disc with angular velocity Ω ≤ 0 or Ω ≥ 1/2 is radial, and both thresholds are sharp.
Continuous rearrangement and symmetry o f solutions of elliptic problems
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Radial symmetry of stationary and uniformly-rotating solutions to the 2D Euler equation in a disc
Every uniformly rotating vortex patch in the unit disc with angular velocity Ω ≤ 0 or Ω ≥ 1/2 is radial, and both thresholds are sharp.