A Representation Formula for the Velocity Part of 3D Time-Dependent Oseen Flows

We prove a representation formula for the solution of an initial-boundary value problem associated with the 3D time-dependent Oseen system. This formula involves the solution of an integral equation on the lateral boundary of the space-time cylinder. The key point of this article is that the assumptions on the data are chosen in such a way that the formula in question may be used in a theory of the asymptotic behaviour of solutions to the nonstationary 3D Navier–Stokes system with Oseen term (incompressible viscous flow in an exterior domain with nonzero velocity at infinity).