Limiting solutions with 90-degree corners for rotating vortex patches

Let $D$ be a rotating vortex patch lying on the global bifurcation curve $\mathscr C$, and let $s$ denote the parameter along this curve. The patches may converge weakly as $s$ tends to infinity.

Limiting-solutions conjecture. The singular solutions with $90$-degree corners seen in numerical computations exist as the weak limits of patches along $\mathscr C$ as $s\to\infty$.

This conjecture formalizes numerical evidence for limiting rotating vortex patches with corner singularities. The source provides no proof or resolution of the asserted limiting behavior.