Nonlinear stability problem of a rotating porous layer
Qin Yu, P. N. Kaloni · Quarterly of Applied Mathematics · 1995
1. Introduction.In hydrodynamic stability theory there are two useful methods, namely, the linear stability method and the energy method.Both of these methods have been used extensively, and, in fact, complement each other.While the linear stability method determines a critical dimensionless bound above which the disturbances of a basic flow are unstable, the energy method predicts a critical bound below which a basic flow is asymptotically stable (in the Liapunov sense).However, in some cases when the linearized system of governing equations happens to be selfadjoint, the linear stability and energy stability predictions coincide (cf.Davis, 1969, Galdi