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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 aunique, global mild solution provided the initial data is small with respect tothe norm the Fourier-Besov space $\dot{FB}_{p,r}^{2-3/p}(\R^3)$, where $p \in(1,\infty]$ and $r \in [1,\infty]$.  In the two-dimensional setting, a unique, global mild solution to this set ofequations exists for {\em non-small} initial data $u_0 \in L^p_\sigma(\R^2)$for $p \in [2,\infty)$.

Global existence results for the Navier-Stokes equations in the rotational framework