Marchioro–Pulvirenti conjecture on the measure of point-vortex collapses

Let ${\mathfrak C}$ be the set of initial data for the point-vortex problem that lead to a collapse in finite time, without assuming the non-neutral cluster hypothesis on the vortex intensities.

Marchioro–Pulvirenti conjecture. The set of collapses ${\mathfrak C}$ has Lebesgue measure $0$.

The conjecture asks whether the improbability-of-collapses theorem remains valid without the non-neutral cluster hypothesis. The existence of unbounded trajectories in finite time is also an open problem.