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Let w be the vorticity of a stationary solution of the two-dimensionalNavier-Stokes equations with a drift term parallel to the boundary in thehalf-plane -\infty<x<\infty, y>1, with zero Dirichlet boundary conditions aty=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 aspecially 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