The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom

In this article we prove a Gevrey class global regularity to the Navier-Sto kes equations on the rotating two dimensional sphere, S-2 - a fundamental m odel that arises naturally in large scale atmospheric dynamics. As a result one concludes the exponential convergence of the spectral Galerkin numeric al method, based on spherical harmonic functions. Moreover, we provide an u pper bound for the number of asymptotic degrees of freedom for this system.