Stability properties of the Boussinesq equations

We consider the stability of equilibrium solutions of tbe Boussinesq equations in an infinite layer R2 x (-1/2, 1/2) heated from below. The equilibria are assumed to be space periodic in the plane direction. Whereas their sitnation is different for nonperiodic disturbance has been studied extensively the situation is different for nonperiodic perturbations. Our interest here is focused on disturbances which are square-integrable in the plane variables. For the motionless state and convection rolls as equilibrium solutions their stability against perturbations in L-squared (R-squared x (-1/2. 1/2)) is compared with their stability against periodic ones. (Author)