Nondegenerate rotating vortex patches are shown to be approximable by smooth compactly supported rotating Euler solutions via a local stream-function construction and Newton's method.
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Non-spherical solutions bifurcate from balls for an unbounded sequence of radii in nonlocal isoperimetric problems, while outside this sequence nearby solutions arise only from rigid motions.
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Desingularization of nondegenerate rotating vortex patches
Nondegenerate rotating vortex patches are shown to be approximable by smooth compactly supported rotating Euler solutions via a local stream-function construction and Newton's method.
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Bifurcations in Isoperimetric Problems with Nonlocal Interactions
Non-spherical solutions bifurcate from balls for an unbounded sequence of radii in nonlocal isoperimetric problems, while outside this sequence nearby solutions arise only from rigid motions.