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In this work, we carry out the asymptotic analysis of the two dimensionalconvective Brinkman-Forchheimer (CBF) equations, which characterize the motionof incompressible fluid flows in a saturated porous medium. We establish theexistence of a global attractor in both bounded (using compact embedding) andPoincar\'e domains (using asymptotic compactness property). In Poincar\'edomains, for $r=1,2$ and $3$, the estimates for Hausdorff as well as fractaldimensions of the global attractors are also obtained. We then show an uppersemicontinuity of global attractors for the 2D CBF equations. We consider anexpanding sequence of simply connected, bounded and smooth subdomains$\Omega_m$ of the Poincar\'e domain $\Omega$ such that $\Omega_m\to\Omega$ as$m\to\infty$. If $\mathscr{A}_m$ and $\mathscr{A}$ are the global attractors ofthe 2D CBF equations corresponding to $\Omega$ and $\Omega_m$, respectively,then we show that for large enough $m$, the global attractor $\mathscr{A}_m$enters into any neighborhood $\mathcal{U}(\mathscr{A})$ of $\mathscr{A}$. Thepresence of Darcy term in the CBF equations helps us to obtain the abovementioned results in general unbounded domains also. Finally, we discuss aboutthe quasi-stability property of the semigroup associated with the 2D CBFequations in bounded domains and establish the existence of finite fractaldimensional global as well as exponential attractors for $r\in[1,\infty)$.

Asymptotic analysis of the 2D convective Brinkman-Forchheimer equations in unbounded domains: Global attractors and upper semicontinuity