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A conditional stability criterion based on generalized energies. (English) Zbl 1114.76022

Summary: An energy criterion for conditional stability is proposed, based on the definition of generalized energies, obtained through a perturbation of the classical \(L^{2}\) (kinetic) energy. This perturbation is such that the contribution of the linear term in the perturbation equation to the generalized energy time derivative is negative definite. A critical amplitude threshold is then obtained by imposing the monotonic decay of the generalized energy. The capabilities of the procedure are appraised through the application to three different low-dimensional models. We also discuss the effects of different choices in the construction of generalized energy on the prediction of critical amplitude threshold in the subcritical regime.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
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