Decay estimates on Besov and Triebel-Lizorkin spaces of the Stokes flows and the incompressible Navier-Stokes flows in half-spaces

Consider the non-stationary Navier-Stokes equation in the upper half space of Rⁿ. We prove the decay estimates of the strong solution and its derivatives in the setting of Besov and Triebel–Lizorkin spaces. This is the first time that the decay estimates of solutions to the non-stationary Navier-Stokes equations on Besov and Triebel-Lizorkin spaces are established. Our results not only extend the known results from Hardy spaces to Besov and Triebel-Lizorkin spaces but also imply new estimates on Sobolev spaces and give better decay estimates on Hardy spaces.