Problems on Small Motions of Systems of Two Viscoelastic Fluids in Fixed Vessels

Abstract

In this paper, we study the problem on small motions of two Oldroyd viscoelastic incompressible fluids contained in a fixed vessel. By means of the operator approach, we reduce the original initial-boundary problem to the Cauchy problem for an operator-differential equation in a Hilbert space and prove the well-posed solvability of the problem on an arbitrary time interval. We deduce the equation for normal oscillations of the considered hydraulic system (the Krein generalized operator pencil).