  We are concerned with the $3$D-Navier-Stokes equations with Coriolis force.
Existence and uniqueness of global solutions in homogeneous Besov spaces are
obtained for large speed of rotation. In the critical case of the regularity,
we consider a suitable initial data class whose definition is based on the
Stokes-Coriolis semigroup and Besov spaces. Moreover, we analyze the asymptotic
behavior of solutions in that setting as the speed of rotation goes to
infinity.
