For every m at least 12, there exist m-fold symmetric uniformly rotating vortex patches whose boundaries have exactly m right-angle corners, proved by a new fixed-point construction.
Steady contiguous vortex-patch dipole solutions of the 2D incompressible Euler equation.Archive for Rational Mechanics and Analysis, 249(46), 2025
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Uniformly Rotating Vortex Patches with 90-Degree Corners
For every m at least 12, there exist m-fold symmetric uniformly rotating vortex patches whose boundaries have exactly m right-angle corners, proved by a new fixed-point construction.