On weighted-norm estimates for nonstationary incompressible Navier–Stokes flows in a 3D exterior domain

Abstract

We study the time-decay of weighted norms of weak and strong solutions to the Navier–Stokes equations in a 3D exterior domain. Moment estimates for weak solutions and weighted L q -estimates for strong solutions are deduced, both of which seem to be optimal. The relation is discussed between the space–time decay and the vanishing of the total net force exerted by the fluid to the body. A class of initial data is given so that the total net force associated to the corresponding fluid flows does not vanish.