  The Cauchy problem for the Navier-Stokes equations with the Coriolis force is
considered. It is proved that a similar a priori estimate, which is derived for
the Navier-Stokes equations by Lei and Lin [11], holds under the effect of the
Coriolis force. As an application existence of a unique global solution for
arbitrary speed of rotation is proved, as well as its asymptotic behavior.
