Boundary layer separation and local behavior for the Steady Prandtl equation

In this paper, we prove the boundary layer separation of the steady Prandtl equation for Oleinik's data ensuring the local existence of the solution under suitable adverse pressure gradient, and confirm Goldstein's hypothesis on the separation rate. We also study the local behavior of the solution near the separation point, which is related to Open problem 5 proposed by Oleinik and Samokhin (P.501, [25]).