A linear magnetic Bénard problem with Hall effect. Application of Budianski-DiPrima method

The influence of the Hall effect on the linear stability of the mechanical equilibrium of a viscous fluid layer heated from below and subject to a constant vertical magnetic field is studied. To this aim, a reformulation of the governing problem as a vector integrodifferential equation enables us to apply the energy method in order to obtain stability criteria. The involved variational problem is solved by the Budiansky-DiPrima method. This method is suitable to complicate boundary conditions, when standard Galerkin type methods are, practically, impossible to apply. It is found that the Hall current has a destabilizing effect.