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In this work, we discuss the large time behavior of the solutions of the twodimensional stochastic convective Brinkman-Forchheimer (SCBF) equations inbounded domains. Under the functional setting$\V\hookrightarrow\H\hookrightarrow\V'$, where $\H$ and $\V$ are appropriateseparable Hilbert spaces and the embedding $\V\hookrightarrow\H$ is compact, weestablish the existence of random attractors in $\H$ for the stochastic flowgenerated by the 2D SCBF equations perturbed by small additive noise. We provethe upper semicontinuity of the random attractors for the 2D SCBF equations in$\H$, when the coefficient of random term approaches zero. Moreover, we obtainthe existence of random attractors in a more regular space $\V$, using thepullback flattening property. The existence of random attractors ensures theexistence of invariant compact random set and hence we show the existence of aninvariant measure for the 2D SCBF equations.

Existence and upper semicontinuity of random attractors for the 2D stochastic convective Brinkman-Forchheimer equations in bounded domains