6 problems

Expanding-ring conjecture. The singular set of the solutions of the cited self-similar Euler construction propagates within the natural symmetry class as the expanding ring…

Consider smooth axisymmetric Euler solutions in the axisymmetric coordinate formulation, with vorticity non-vanishing on the axis of symmetry. Artificial-boundary conjecture. There…

Radial smoothness conjecture. The initial vorticity $\omega_0$ can be $C^\infty$ as a function of $\rho$. This sharpens the preceding conjecture by requiring the lack of regularity…

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 b…

Let $(r,z)$ belong to the cylindrical domain $\{(r,z):0\leq r\leq1\}$. Hou–Luo conjecture. There exists a smooth solution to the axisymmetric Euler equation on this cylindrical dom…

Let $T_*<\infty$ and let $\omega\in C^\infty_c(\mathbb{R}^3\times[0,T_*))$ be a smooth solution of the 3D Euler equation that becomes singular as $t\to T_*$. Minimal-intensity conj…