For every m at least 2, the paper constructs uniformly rotating Euler vortex-patch solutions with one outer patch and m small negative inner patches that collapse to a central point vortex as epsilon tends to zero.
Uniformly rotating smooth solutions for the in- compressible 2d Euler equations.Archive for Rational Mechanics and Analysis, 231(2):719–785, 2019
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Uniformly Rotating Euler Configurations with Multiple Vorticity Holes
For every m at least 2, the paper constructs uniformly rotating Euler vortex-patch solutions with one outer patch and m small negative inner patches that collapse to a central point vortex as epsilon tends to zero.