Topological approximation approach to study of mathematical problems of hydrodynamics

We give a description of an abstract scheme of the topological approximation method and mention those fields where its application to concrete models of hydrodynamics yields results. As an illustration, we expose in detail the problem of optimal control of right-hand sides in the initialboundary value problem describing the motion of a viscoelastic incompressible fluid in the Jeffreys model with the Jaumann objective derivative.