Homogeneous model of incompressible viscoelastic fluid of the non-zero order

The paper deas with the Cauchy–Dirichlet problem for homogeneous dynamics model of the incompressible viscoelastic Kelvin–Voigt fluid of the non-zero order. The problem is studed using the theory of semilinear Sobolev type equations. The Cauchy–Dirichlet problem for the corresponding system of differential equations in partial derivatives is reduced to the abstract Cauchy problem for the indicated equations. The theorem of unique existance of solution to indicated problem, which is a quasistationary trajectory, is proved. The phase space is described.