Liouville Theorems for Stationary Navier-Stokes Equations via the Radial Velocity Component

We study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the velocity, namely $u_ρ(x) \in L^p(\mathbb{R}^3)$ with $3/2 < p \l