The basis of the Falkner-Skan approach are the Prandtl boundary layer equations.  Ludwig Prandtl  simplified the equations for fluid flowing along a wall (wedge) by dividing the flow into two areas: one close to the wall dominated by viscosity, and one outside this near-wall boundary layer region where viscosity can be neglected without significant effects on the solution. This means that about half of the terms in the Navier-Stokes equations are negligible in near-wall boundary layer flows (except in a small region near the leading edge of the plate). This reduced set of equations are known as the Prandtl boundary layer equations. For steady incompressible flow with constant viscosity and density, these read:
Mass Continuity: 
-Momentum: 
-Momentum: 
Here the coordinate system is chosen with  pointing parallel to the plate in the direction of the flow and the  coordinate pointing towards the free stream,  and  are the  and  velocity components,  is the pressure,  is the density and  is the kinematic viscosity.
A number of similarity solutions to these equations have been found for various types of flow. Falkner and Skan developed the similarity solution for the case of laminar flow along a wedge in 1930. The term similarity refers to the property that the velocity profiles at different positions in the flow look similar apart from scaling factors in the boundary layer thickness and a characteristic boundary layer velocity. These scaling factors reduce the partial differential equations to a set of relatively easily solved set of ordinary differential equations.