| Abstract: |
| The flow of a fluid through a porous medium is classically described by Darcy`s law. However, it typically applies for sufficiently slow viscous flows, e.g.\ for flows with small Reynolds numbers (laminar flows). When the flow is non-Darcian (e.g.\ turbulent flows), various modifications of Darcy`s law are used to describe it. In this talk, we will discuss one such model, namely the convective Brinkman--Forchheimer equations (CBF). From the mathematical perspective, this model can be seen also as the incompressible Navier--Stokes equations with damping term $|v|^{r - 1}v$, called the absorption term (or the Forchheimer term). We will give an overview of some available results for this model, focusing mainly on energy equality in the `critical` case $r = 3$ on periodic domains. To handle more general bounded domains we use an abstract simultaneous approximation scheme which will be the main focus of this talk. |
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