A nonlinear hydrodynamic stability criterion derived by a generalized energy method

By applying a new variant of the A. Georgescu – L. Palese – A. Redaelli (G-P-R) method [8], based on the symmetrization of a linear operator, we deduce a nonlinear stability criterion of a state of thermal conduction of a horizontal fluid layer subject to a vertical upwards uniform magnetic field and a vertical upwards constant temperature gradient. The Boussinesq approximation is used. The upper and lower surfaces of the layer are two rigid walls. It is assumed that the magnetic Prandtl number is strictly greater than unity.