A boundary value problem for one overdetermined system arising in two-velocity hydrodynamics

In the half-plane $R^2$ , we consider a stationary system of two-velocity hydrodynamics with one pressure and homogeneous divergent and boundary conditions for two velocities. The system is overdetermined. The solution to this system is reduced to a consistent solution of the two boundary value problems: the Stokes problem for one velocity and pressure and the overdetermined system for a different velocity. For an appropriate choice of function spaces, the existence and uniqueness of the generalized solution with a corresponding stability estimate is proven.