Weighted estimate of the asymptotic profiles of the Navier–Stokes flow in Rn

We study the asymptotic profiles of the Navier–Stokes flow and the weighted estimate of the spatial and temporal decay rate of the error term. This paper extends the result of Y. Fujigaki and T. Miyakawa in [Y. Fujigaki, T. Miyakawa, Asymptotic profiles of nonstationary incompressible Navier–Stokes flows in the whole space, SIAM J. Math. Anal. 33 (3) (2001) 523–544], where they derived the asymptotic profiles of the Navier–Stokes flow and estimated the temporal decay rate of the error term.