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

We prove a Gevrey class global regularity of the Navier-Stokes equations on a rotating two dimensional sphere, a fundamental model that arises naturally in large scale atmospheric dynamics. The result demonstrates the exponential convergence of the spectral Galerkin numerical method based on spherical harmonic functions. Moreover, we provide an upper bound for the number of asymptotic degrees of freedom for this system. (Author)