Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media

<p style='text-indent:20px;'>We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample porous medium. Specifically, we introduce and analyze 3D Brinkman-Forchheimer-Bénard problem describing the behavior medium between two plates heated from bottom cooled top. We show existence uniqueness global in-time solutions, absorbing balls <inline-formula><tex-math id="M1">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula> id="M2">\begin{document}$ H^1 $\end{document}</tex-math></inline-formula>. Eventually, comment on applicability data assimilation algorithm to our system.</p>