2 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…

Let $u^0\not\equiv 0$ belong to $H^s_{as\&df}(\mathbb{R}^3)$ with $s>\frac{5}{2}$, and let $\omega^0$ be its associated vorticity. Assume that $\omega^0$ is odd in $z$ and satisfie…