Why should the pressure across the Boundary Layers konstant?

(1). In 1904 Prandtl developed the boundary layer theory for high Reynolds numbers flow. At high Reynolds number, the viscous flow is confined to the small layer next to the wall. (2). Based on this, (see chapter on laminar boundary layer of the book written by Schlchting,"boundary layer theroy"), equations 7.1,7.2, the normal pressure gradient in the normal momentum-equation is small. (3). After integration across the boundary layer, the pressure difference is very small, (small)^2. So, it is assumed that the pressure can be considered as constant(assumed), and it can be specified at the edge of the boundary layer. This simplifies the equations and the solution procedure to solve the boundary layer equations. (4). This is not the case at high Mach number, at the leading edge region, or at lower Reynolds number.