Abstract
An analog of the classical Couette problem for the motion of an incompressible viscoelastic Kelvin–Voigt medium in a gap between two coaxial cylinders is considered. The external cylinder is fixed, whereas the internal cylinder is rotating either forcedly with a constant velocity or inertially. The unique solvability is proved in both cases. An analogy between the propagation of acoustic cylindrical waves in a viscous gas and transversal waves in a Kelvin–Voigt medium moving along circular trajectories is discussed. The asymptotic behavior of solutions is also studied. It is shown that the limit regime can be monotone or oscillatory in dependence on the parameters of the problem. Bibliography: 11 titles. Illustrations: 2 figures.
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