Approximation of stationary statistical properties of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics

Abstract

The main objective of this paper is to study the temporal approximation scheme of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics. We first prove the existence of a global attractor in V by using the Sobolev compactness embedding theorem, and then we prove its global attractor and stationary statistical properties of the temporal approximation scheme convergence to those of the three-dimensional primitive equations of large-scale ocean and atmosphere dynamics as the time step goes to zero.