Global Bifurcation of Rotating Vortex Patches

  title={Global Bifurcation of Rotating Vortex Patches},
  author={Zineb Hassainia and Nader Masmoudi and Miles H. Wheeler},
  journal={Communications on Pure and Applied Mathematics},
We rigorously construct continuous curves of rotating vortex patch solutions to the two‐dimensional Euler equations. The curves are large in that, as the parameter tends to infinity, the minimum along the interface of the angular fluid velocity in the rotating frame becomes arbitrarily small. This is consistent with the conjectured existence [30, 38] of singular limiting patches with 90 corners at which the relative fluid velocity vanishes. For solutions close to the disk, we prove that there… 

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