Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

TL;DR

This paper investigates the long-term behavior of solutions to the three-dimensional viscous primitive equations modeling large-scale moist atmosphere, establishing the existence of global and exponential attractors and analyzing their fractal dimensions.

Contribution

It proves the existence of global and exponential attractors for these equations and determines the finiteness of their fractal dimensions, advancing understanding of atmospheric dynamics.

Findings

Existence of a global attractor for the system.

Construction of an exponential attractor using smoothing properties.

Finite fractal dimension of the global attractor.

Abstract

This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere. As a byproduct, we obtain the fractal dimension of the global attractor for the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere is finite, which is in consistent with the results in \cite{jn2,jn1}.