Global well-posedness of a three-dimensional Brinkman-Forchheimer-B\'enard convection model in porous media

TL;DR

This paper proves the global well-posedness of a 3D Brinkman-Forchheimer-Bénard convection model in porous media, establishing existence, uniqueness, and long-term behavior of solutions, with implications for data assimilation.

Contribution

It introduces and analyzes a new 3D convection model in porous media, proving global existence, uniqueness, and long-term stability of solutions.

Findings

Existence of global in-time solutions

Uniqueness of solutions

Existence of absorbing balls in L^2 and H^1

Abstract

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-B\'enard 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 $L^2$ and $H^1$. Eventually, we comment on the applicability of a data assimilation algorithm to our system.