DECAY ESTIMATES FOR STEADY SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN TWO DIMENSIONS IN THE PRESENCE OF A WALL

Let omega 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 Omega(+) = {(x, y) is an element of R-2 vertical bar y > 1}, with zero Dirichlet boundary conditions at y = 1 and at infinity, and with a small force term of compact support. Then vertical bar xy omega(x, y)vertical bar is uniformly bounded in Omega(+). The proof is given in a specially adapted functional framework, and the result is a key ingredient for obtaining information on the asymptotic behavior of the velocity at infinity.