Abstract
The nonlinear stability of laminar flow, in the x-direction, between two parallel planes in the presence of a coplanar magnetic field has been studied using Lyapunov direct method with either rigid or stress-free boundary planes. By defining a Lyapunov function it is proved that the laminar solutions of the system are nonlinearly unconditionally and asymptotically stable for all Reynolds numbers and magnetic Reynolds numbers if the perturbations are two-dimensional and depend only on y, z and t.
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