Well-posedness and regularity of the Darcy-Boussinesq system in layered porous media

Abstract

We establish the existence of global weak solution in 2D and 3D, as well as the uniqueness of weak solution in 2D, for the Darcy-Boussinesq model for convection in layered porous media with square integrable initial data. We also derived tangential regularity in the 2D case. In addition, we obtain the existence and uniqueness of regular solution in a novel piecewise $H^2$ space in both 2D and 3D under uniform porosity assumption and $H^1$ initial data. This is the first rigorous result for this model in the physically important layered setting.