We prove Liouville-type theorems for the stationary incompressible Navier-Stokes and MHD equations in \(\mathbb {R}^{3}\) under certain growth conditions at far annulus field. Precisely, let the potential tensor function V satisfy that \(\nabla \cdot {V}=u\) for a smooth solution u of the stationary Navier-Stokes equations, we show that if the \(L^{s}\) mean oscillation of the potential V on the annulus at infinity satisfies suitable growth condition, then u must be zero. Furthermore, the triviality of u and b for the MHD equations can also be guaranteed under additional growth condition of certain Lorentz norms for the magnetic field.
