5 problems

Consider axisymmetric Euler flow without swirl, with initial vorticity consisting of two anti-parallel vortex rings … where $f\geq 0$ is localized near $(r_0,z_0)$ with $r_0>0$ and…

Longer-time approximation conjecture. An approximation result of the form $$

Uniqueness extension conjecture. The uniqueness theorem for these steady vortex rings should also hold when

Nonexistence conjecture. When $m-n>1$, there will be no balancing configurations satisfying those requirements.

Let $n$ be the number of vortices and consider the regular $n$-gon at the bifurcation point, with stability determined by the positivity of the relevant quadratic form. Stability c…