The Hou–Luo finite-time singularity conjecture for axisymmetric Euler flow

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 domain that becomes singular in finite time. This conjecture is motivated by the Hou–Luo scenario and numerical evidence, but a rigorous proof remains open.