Prediction-control problem for some systems of equations of fluid dynamics

By methods of the theory of degenerate semigroups of operators, we investigate inverse problems for some systems of equations of fluid dynamics containing the incompressibility equation ? · v = 0. Namely, we obtain well-posedness criteria for inverse problems for the system of Sobolev equations, which describes the dynamics of small internal motions of a stratified fluid in an equilibrium state under some additional assumptions, and for the system of Oskolkov equations, which, in the linear approximation, describes the dynamics of a viscoelastic incompressible Kelvin-Voigt fluid of order 1.