Analysis of the class of hydrodynamic systems

The solvability of the Cauchy-Dirichlet problem for the generalized homogeneous model of the dynamics of the high-order viscoelastic incompressible Kelvin-Voigt fluid is considered. In the study, the theory of semilinear equations of the Sobolev type was used. The indicated problem for the system of differential equations in partial derivatives is reduced to the Cauchy problem for the indicated type of the equation. The theorem on the existence of the unique solution of this problem, which is a quasi-stationary trajectory, is proved, and its phase space is described.