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

Abstract

Using the Stokes solution formula and Lq–Lr 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∞(R+n)→Lσ∞(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.