LOCAL AND GLOBAL EXISTENCE RESULTS FOR THE NAVIER-STOKES EQUATIONS IN THE ROTATIONAL FRAMEWORK

Consider the equations of Navier-Stokes in R-3 in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided only the horizontal components of the initial data are small with respect to the norm the Fourier-Besov space FBp,r2-3/(p) (R-3), where p is an element of [2, infinity] and r is an element of [1, infinity).