On the solvability of boundary problems for stationary Navier-Stokes equations

The boundary value problems for Navier-Stokes equations describing the steady-state incompressible viscous homogeneous flow in bounded domain are considered. The boundary conditions are the boundary value of the total pressure, tangential and normal components of the flow velocity and vorticity. The unilateral boundary problems are also examined. The main aims of the paper are 1) to prove the solvability of nonhomogeneous boundary problems for any Reynold's number, 2) to prove the solvability of homogeneous boundary problems in case of the domain with piecewise smooth boundary.