Abstract:

Many natural and engineering problems involve the study of flow and convection in a system that couples  free-flow and porous media flow. In this talk, we present a few recent results on the Navier-Stokes-Darcy-Boussinesq equation which models the coupled system. In particular, the well-posedness of the model under appropriate interface conditions, the onset of convection at large enough Rayleigh number, and the decoupling of the subsystems at small Darcy number will be discussed.