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Bifurcation of rotating patches from Kirchhoff vortices

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  • In this paper we investigate the existence of a new family of rotating patches for the planar Euler equations. We shall prove the existence of countable branches bifurcating from the ellipses at some implicit angular velocities. The proof uses bifurcation tools combined with the explicit parametrization of the ellipse through the exterior conformal mappings. The boundary is shown to belong to Hölderian class.
    Mathematics Subject Classification: Primary: 35Q31; Secondary: 35Q35, 76B03.


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