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

Consider the equations of Navier–Stokes in \(\mathbb{R}^3\) 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 \(FB^{{2-3}/p}_{p,r}(\mathbb{R}^3)\), where \(p\; \in \; (1,\infty]\; \mathrm{and}\; r\;\in [1,\infty]\). In the two-dimensional setting, a unique, global mild solution to this set of equations exists for non-small initial data \(u_{0} \; \in \;L^p_{\sigma}(\mathbb{R}^2)\;\mathrm{for}\;p \;\in\;[2,\infty).\)