Equations of the boundary layer for a modified Navier–Stokes system

We consider a system of equations of the boundary layer derived from the hydrodynamical system for generalized Newtonian media. This modification of the Navier–Stokes system was proposed by O. A. Ladyzhenskaya in connection with the uniqueness of the solution of this system in general. We prove the existence and the uniqueness of a solution for the problem of continuation of the boundary layer and consider some questions connected with the separation of the boundary layer.