Global weak solutions to the Navier-Stokes-Darcy-Boussinesq system for thermal convection in coupled free and porous media flows

We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we prove existence of global weak solutions to the initial boundary value problem subject to the Lions and Beavers-Joseph-Saffman-Jones interface conditions. The proof is based on a proper time-implicit discretization scheme combined the compactness argument. Next, we establish a weak-strong uniqueness result such that a weak solution coincides with a strong solution emanating from the same initial data as long as the latter exists.