Global Attractors for the Three-Dimensional Tropical Climate Model with Damping Terms

Abstract

In this paper, we consider the 3D tropical climate model with damping terms in the equation of u, v and \(\theta \), respectively. Firstly, we get some uniform estimates of strong solution. Secondly, we derive the result of the continuity of the semigroup \(\{S(t)\}_{t\ge 0}\) in case of \(4\le \alpha ,\beta <5\) and \(\frac{13}{5}<\gamma <5\) via some usual inequalities. Finally, the system (1.1) is shown to possess an \(({\mathbb {V}},{\mathbb {V}})\)-global attractor and an \(({\mathbb {V}},{\textbf{H}}^{2})\)-global attractor.