A Boundary Value Problem for an Overdetermined Steady System in Two-Velocity Hydrodynamics

In this paper, a two-velocity steady hydrodynamic system with a single pressure and inhomogeneous divergent and boundary conditions for two velocities is investigated. This system is overdetermined. By changing the sought-for functions, the problem is reduced to a homogeneous one. The resulting system is solved by consecutively solving two boundary value problems: a Stokes problem for one velocity and the pressure and an overdetermined system for the other velocity. Generalized statements of these problems and their discrete approximations using a finite element method are presented. A new regularization method is used to solve the overdetermined problem.