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

In the half-plane $R^2_+$ we consider a stationary system of two-velocity hydrodynamics with one pressure and homogeneous divergent and inhomogeneous boundary conditions for two velocities. Such system is overridden. The solution to this system is reduced to the sequential solution of two boundary value problems: the Stokes problem for one velocity and pressure and an overdetermined boundary value problem for the vector Poisson equation for the other speed. With an appropriate choice of function spaces, the existence and uniqueness are proven for generalized solution with the corresponding stability estimate.