Large Time Behavior of Deterministic and Stochastic 3D Convective Brinkman-Forchheimer Equations in Periodic Domains

The large time behavior of deterministic and stochastic three dimensional convective Brinkman-Forchheimer (CBF) equations $$\begin{aligned} \partial _t{\varvec{u}}-\mu \Delta {\varvec{u}}+({\varvec{u}}\cdot \nabla ){\varvec{u}}+\alpha {\varvec{u}}+\beta |{\varvec{u}}|^{r-1}{\varvec{u}}+\nabla p={\varvec{f}},\ \cdot {\varvec{u}}=0, \end{aligned}$$ ∂ t u - μ Δ + ( · ∇ ) α β | r 1 p = f , 0 for $$r\ge 3$$ ≥ 3 $$\mu ,\beta >0$$ > $$r>3$$ $$2\beta \mu \ge 1$$ 2 $$r=3$$ ), in periodic domains is carried out this work. Our first goal to prove the existence global attractors 3D CBF equations. Then, we show random perturbed by small additive smooth noise. Furthermore, establish upper semicontinuity (stability attractors), when coefficient perturbation approaches zero. Finally, address uniqueness invariant measures