Dynamic of the three dimensional viscous primitive equations of large-scale atmosphere

Abstract

The main objective of this paper is to study the existence of a finite dimension global attractor for the three dimensional viscous primitive equations of large-scale atmosphere. Thanks to the shortage of the uniqueness of weak solutions, we prove the existence of a global attractor with finite fractal dimension for the three dimensional viscous primitive equations of large-scale atmosphere by using the method of $\ell$-trajectories.