The supercritical NLS standing-vortex blowup conjecture

Let $\psi(t,r,\theta)=A(t,r)e^{imtheta}$ be a singular standing-vortex solution of the two-dimensional NLS with $\sigma>2$, and let $\psi_F$ denote the radial self-similar profile. Supercritical NLS standing-vortex conjecture. The solution blows up with asymptotic profile

$$\psi\sim e^{im\theta}\cdot\psi_F(t,r),$$

where $\psi_F$ is the profile specified in the source, and the three assertions of the supercritical NLS standing-ring conjecture hold. This predicts that the vortex phase does not alter the one-dimensional peak-collapse dynamics; the parser supplies no resolution evidence.