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

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