Radial smoothness conjecture for axisymmetric Euler blow-up

Let $\omega_0$ be the initial vorticity in the preceding subcritical Hölder blow-up conjecture, and write

$$\rho=\sqrt{x_1^2+x_2^2+x_3^2}.$$

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 only in the flow direction; it remains open.