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

Abstract

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 the Fourier-Besov space ${\dot{FB}}_{p,r}^{2-3/p}({\mathbb{R}}^3)$, where $p\in (1,\infty ]$ and $r\in [1,\infty ]$. In the two-dimensional setting, a unique, global mild solution to this set of equations exists for {\em non-small} initial data $u_0\in L_{\ddot{I}}^pƒ({\mathbb{R}}^2)$ for $p\in [2,\infty )$.