These equations are non-linear. However assumptions of boundary layer theory make solution procedure simpler. Apart from this the pressure is only function of X-coordinate hence can be represented using an ordinary differential equation rather than a partial differential equation.The variables u, v, p, ρ, T and h are the unknowns in these equations. However, p can be known from p=p_e(x). Rest of the variables likeµ and κ are properties of fluid and are temperature dependant. The following perfect gas relations should also be used to complete the set of equations.

Boundary conditions to be considered to solve above equations are

Here subscript e stands for the values measured or known at the edge of the boundary layer. The boundary layer equations are valid for compressible subsonic or supersonic flow. In case of application for hypersonic flows, it should again be noted that the Y-momentum equation should be changed for high Mach number cases.