Summary: A model system of nonlinear equations is considered, differing from the system of equations of the three-dimensional boundary layer of an incompressible fluid only in the fact, that in the equations of motion the component v of the velocity vector along the normal to the body is replaced by the value of this function in some region of diameter not larger than \(2\epsilon\), \(\epsilon\)-averaged over the spatial coordinates. Since the function v represents the limit of averaging as \(\epsilon\to 0\), it is likely that for sufficiently small \(\epsilon\) the solution of the system in question will differ by an arbitrarily small amount from the solution of the system of equations of the three- dimensional boundary layer (the problem of convergence towards this solution is not investigated).
It is shown that when the components of the pressure gradient are negative and the conditions of adhesion or suction at the surface of the body hold, the model system of equations in question has, for any \(\epsilon >0\), not more than one solution and possesses definitely the zones of influence and dependence which are assigned, without proper mathematical justification, to the boundary layer flows on the basis of physical considerations or computations. In addition, an explicit estimate is given independent of \(\epsilon\), for the distribution of the zones shown, depending on the initial and boundary perturbations of the flow.