Global Existence Results for the Navier-Stokes Equations in the Rotational Framework in Fourier-Besov Spaces

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 the initial data is small with respect to the norm of the Fourier-Besov space (F)over dot B-p,r(2-3/p) (R-3), where p is an element of (1, infinity] and r is an element of [1, infinity]. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data u(0) is an element of L-sigma(p)(R-2) for p is an element of [2, infinity).