The subcritical Hölder blow-up conjecture for axisymmetric Euler flow

Let $\alpha<1/3$. Subcritical Hölder blow-up conjecture. There exists a compactly supported, axisymmetric, no-swirl local Euler solution with initial regularity $C^\alpha_c$ that becomes singular in finite time. The source notes that $C^{1/3+}_c$ solutions are globally regular, so this conjecture would close the known regularity gap; it remains open.