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On the nonlinear stability of the magnetic Bénard problem with rotation. (English) Zbl 0798.76028

Summary: The nonlinear stability of the magnetic Bénard problem with rotation is studied through the Lyapunov direct method. It is shown that, in the stress-free case and for vanishing stress at the boundaries, the nonlinear critical Rayleigh number has the same behaviour as in the linear case. In particular, for a stationary convection, it shows an initial decrease with the Chandrasekhar number \(Q^ 2\) and for large \(Q^ 2\) it goes to infinity as \(Q\).

MSC:

76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30 Nonlinear effects in hydrodynamic stability
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