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

## TL;DR

This paper proves the existence of a finite-dimensional global attractor for the 3D viscous primitive equations modeling large-scale atmospheric dynamics, addressing challenges due to weak solution uniqueness.

## Contribution

It introduces a novel approach using $ ext{ extlangle}$-trajectories to establish finite-dimensional global attractors despite weak solution non-uniqueness.

## Key findings

- Existence of a finite-dimensional global attractor proven.
- Method applicable despite weak solution non-uniqueness.
- Advances understanding of long-term behavior of atmospheric models.

## 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.