Lower bound of L2 decay of the Navier-Stokes flow in the half-space R+n and its asymptotic behavior in the frequency space

We consider the asymptotic behavior of weak solutions of the Navier-Stokes equations in the half-space R+n. We obtain the lower bound of the energy decay of the Navier-Stokes flow, by means of the profile of the initial data. Indeed, we construct a class of the initial data which causes the slow decay of the Navier-Stokes flow, with an explicit rate. Furthermore, we investigate the asymptotic behavior of concentration in the frequency space.