Estimation of the Decay of Perturbations Imposed on an Accelerating Viscoplastic Couette Flow

Abstract

In this study, an unsteady one-dimensional shear in a flat layer of a viscoplastic medium is chosen as the main flow for which there are no hard layers in the transverse direction. Such a velocity profile is implemented, for example, in the Couette flow accelerating under the action of the acceleration of one of the boundaries. On the basis of the integral-equation method, the integral estimates of the exponential decay of the initial perturbations are derived with the H₂ space metrics.