Finite-energy steady planar Euler flows with connected stagnation set are governed by a single semilinear elliptic equation, and become circular when the vorticity has no local extrema outside a large ball.
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Rigidity results for finite energy solutions to the stationary 2D Euler equations
Finite-energy steady planar Euler flows with connected stagnation set are governed by a single semilinear elliptic equation, and become circular when the vorticity has no local extrema outside a large ball.