Vorticity growth beyond bounded relative vorticity for axisymmetric Euler flows without swirl

We establish upper bounds for vorticity and related quantities in axisymmetric Euler flows without swirl in $\mathbb{R}^3$, assuming that the initial relative vorticity $ω_0/r$ belongs to $L^1\cap L^p$ with $3<p\le \infty$. For each fixed $p \in (3,\infty]$, we obtain polynomial-in-time upper bounds