Decay estimates for steady solutions of the Navier-Stokes equations in two dimensions in the presence of a wall

Abstract

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.

New version (3rd October 2011): more detailed introduction, with new references (including follow-up paper); revisited structure slightly; additional details to the mathematical properties of the non-linear terms