Asymptotic behavior for the Navier–Stokes equations with nonzero external forces

We estimate the asymptotic behavior for the Stokes solutions, with external forces first. We found that if there are external forces, then the energy decays slowly even if the forces decay quickly. Then, we also obtain the asymptotic behavior in the temporal-spatial direction for weak solutions of the Navier–Stokes equations. We also provide a simple example of external forces which shows that the Stokes solution does not decay quickly.