Weighted decay properties for the incompressible Stokes flow and Navier-Stokes equations in a half space

Using the Stokes solution formula and L-q-L-r estimates of the Stokes operator semigroup, we establish the weighted decay properties for the Stokes flow and Navier-Stokes equations including their spatial derivatives in half spaces. In addition, the unboundedness of the projection operator P: L-infinity(R-+(n)) -> L-sigma(infinity)(R-+(n)) is overcome by employing a decomposition for the nonlinear term, and L asymptotic behavior for the second derivatives. of Navier-Stokes flows in half spaces is given. (C) 2012 Elsevier Inc. All rights reserved.