A BOUNDARY VALUE PROBLEM FOR ONE OVERDETERMINED SYSTEM ARISING IN TWO–VELOCITY HYDRODYNAMICS

In the half-plane R2 , 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.

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