On the nonlinear stability of the magnetic Benard problem with rotation

The direct Liapunov method was used to study the nonlinear stabiity of the magnetic Benard problem with rotation. It is shown that, for stress-free boundary conditions and when magnetic stress vanishes at the boundaries, the nonlinear critical Rayleigh number has the same behavior as in the linear case. In particular, for a stationary convection, it exhibits an initial decrease with the Chandrasekhar number, Q sup 2, and for large Q sup 2 it yields infinity as Q.