Approximate solutions for Dorodnitzyn's gaseous boundary layer limit formula

Abstract

Oleinik's no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R ⊂ R 2 . It also allowed us to find a limit formula for Dorodnitzyn's stationary compressible boundary layer with constant total energy on a bounded convex domain in the plane R 2 . Under the same assumption, we can give an approximate solution u for the limit formula if |u|< < < 1 such that:that corresponds to an approximate horizontal velocity component when a small parameter ǫ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, c > 0, δ is the boundary layer's height in Dorodnitzyn's coordinates, U is the free-stream velocity at the upper boundary of the domain, and T 0 is the absolute surface temperature.