Lower bound of decay of the Navier–Stokes flow in the half-space 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.