Couette Problem for Kelvin–Voigt Medium

The analogue of classical Couette problem for incompressible viscoelastic Kelvin–Voigt medium motion in the gap between two coaxial cylinders is investigated. External cylinder is fixed, while the internal one is either rotating forcedly with a constant velocity or rotating inertially. Unique solvability is proved for both problems. The analogy between propagation of acoustic cylindrical waves in viscous gas and transversal waves in Kelvin–Voigt medium which appear during its motion along circular trajectories is found. The asymptotic behavior of solution stabilization to Couette motion in the first problem and inertial cylinder motion approaching to equilibrium state were studied. Both monotonous and oscillatory regimes of quiescent state approaching are possible subject to problem parameters.