Beyond the $L^{9/5}$ Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem

Let $(v,p)$ be a smooth stationary Navier--Stokes solution in $\mathbb R^3$ with $v(x)\to0$ as $|x|\to\infty$. We prove that $v\equiv0$ if its vorticity $ω:= \nabla\times v$ belongs to $L^{s,\infty}(\mathbb R^3)$ for some $9/5\le s<(2+\sqrt{13})/3$. To the author's knowledge, this is the first globa