A stability result for the Stokes-Boussinesq equations in infinite 3d channels

Abstract

We consider the Stokes-Boussinesq (and the stationary Navier-Stokes-Boussinesq) equations in a slanted, i.e. not aligned with the gravity's direction, 3d channel and with an arbitrary Rayleigh number. For the front-like initial data and under the no-slip boundary condition for the flow and no-flux boundary condition for the reactant temperature, we derive uniform estimates on the burning rate and the flow velocity, which can be interpreted as stability results for the laminar front.