RESUMEN

Sufficient conditions for the monotone decay of disturbances to oscillatory and steady Hagen–Poiseuille flow are rigorously derived within the framework of linear stability theory. The conditions hold both for axisymmetric and nonaxisymmetric disturbances, whereas the result for

nonaxisymmetric disturbances to the oscillatory flow is of particular importance because in this case even numerical results are not available in the literature. Furthermore, the conditions provide explicit bounds on the range of parameters that must be examined in any prospective search for instability by numerical means. The derivation of the sufficient conditions on monotone decay is based on a detailed analysis of the spectrum of the Stokes operator.