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.
Doubly connectedV-states for the planar Euler equations.SIAM Journal on Mathematical Analysis, 48(3):1892–1928, 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.