Approximation of time-periodic flow past a translating body by flows in bounded domains

We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain Ω R³ that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains Ω BR, incorporating appropriate artificial boundary conditions on BR. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius R, showing that, as R, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow.