Porous MHD Convection: Effect of Vadasz Inertia Term

The onset of porous convection in an electrically conducting fluid uniformly heated from below and embedded in an external transverse constant magnetic field is analysed. In particular the effect of Vadasz inertia term, measured through the Vadasz number Va, on the instability threshold, is investigated. For the three-dimensional perturbations and full nonlinear problem it is shown that sub-critical instabilities do not exist and the global nonlinear stability is guaranteed by the linear stability. The long-time behaviour is characterized via the existence of L2-absorbing sets.