A remark on a priori estimate for the Navier-Stokes equations with the Coriolis force

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.