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

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}.