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

Abstract 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 $$\Omega \subset {\mathbb {R}}^3$$ 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 $$\Omega \cap B_R$$ , incorporating appropriate artificial boundary conditions on $$\partial B_R$$ . 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 $$R \rightarrow \infty $$ , the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow.