abstract
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We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-Bnard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in
and\begin{document}$ L^2 $end{document} . Eventually, we comment on the applicability of a data assimilation algorithm to our system.\begin{document}$ H^1 $end{document}