Quasistationary trajectories of the Taylor problem for the model of the incompressible viscoelastic liquid of the nonzero order

Taylor's problem for the model of the dynamics of the Kelvin–Voight incompressible viscoelastic liquid of the nonzero order is considered. This problem is investigated in the frames of the theory of the semilinear Sobolev type equations. The theorem of the existence of the unique solution of this problem is proved and the description of its phase space is received.