  Existence, uniqueness, and regularity of time-periodic solutions to the
Navier-Stokes equations in the three-dimensional whole-space are investigated.
We consider the Navier-Stokes equations with a non-zero drift term
corresponding to the physical model of a fluid flow around a body that moves
with a non-zero constant velocity. Existence of a strong time-periodic solution
is shown for small time-periodic data. It is further shown that this solution
is unique in a large class of weak solutions that can be considered physically
reasonable. Finally, we establish regularity properties for any strong solution
regardless of its size.
