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