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.
An analytical and numerical study of steady patches in the disc.Analysis & PDE, 9(7):1609–1670, 2016
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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.