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Let w be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane -infty<x<infty, y>1, with zero Dirichlet boundary conditions at y=1 and at infinity, and with a small force term of compact support. Then, |xyw(x,y)| is uniformly bounded in the half-plane. The proof is given in a specially adapted functional framework and complements previous work

Decay Estimates for Steady Solutions of the Navier--Stokes Equations in Two Dimensions in the Presence of a Wall