Existence and uniqueness of slightly compressible Boussinesq's flow in Darcy-B\'enard problem

Abstract

In the present paper, we study the existence, uniqueness and behaviour in time of the solutions to the Darcy-B\'enard problem for an extended-quasi-thermal-incompressible fluid-saturated porous medium uniformly heated from below. Unlike the classical problem, where the compressibility factor of the fluid vanishes, in this paper we allow the fluid to be slightly compressible and we address the well-posedness analysis for the full nonlinear initial boundary value problem for the perturbed system of governing equations modelling the convection in porous media phenomenon.