In the domain Ω, external to a bounded domain Ω′ ⊂ \({\mathbb{R}}^{2}\) , we consider a stationary overdetermined system of two-velocity hydrodynamics with one pressure and homogeneous divergent and inhomogeneous boundary condition for two velocities. The solution of this system is reduced to successive solving two boundary value problems: the Stokes problem for one velocity and pressure and an auxiliary overdetermined boundary value problem for the vector Laplace equation for the other velocity. We establish the existence and uniqueness of a generalized solution to the system and derive the stability estimate.
