This is a joint Analysis of Fluids & Related Topics and Analysis seminar.  We give a rigorous proof of the speed at which Boundary layer separation occurs in Prandtl system.  In particular this justifies a heuristic rate proposed by Landau and formal asymptotic expansions proposed by Goldstein and Stewartson. The proof is based on the construction of an approximate solution, energy estimates and maximum principle.  Joint work with Anne-Laure Dalibard (UPMC).