Global well-posedness for the 3-D incompressible anisotropic rotating Navier-Stokes equations.

We investigate the Cauchy problem for the three-dimensional incompressible anisotropic rotating Navier-Stokes equations. Specifically, the aim of this paper is twofold: first, we prove that this system admits a unique, global solution provided that the initial datum is small with respect to the norm of the critical spcace $ B^{-\frac{1}{2},\frac{1}{2}}_{4}(\mathbb{R}^{3}) $. Second, we consider the asymptotic behaviour of solution $ u^{\varepsilon} $when the Rossby number $ \varepsilon $ goes to zero. [ABSTRACT FROM AUTHOR]