  In this paper, we prove that separation occurs for the stationary Prandtl
equation, in the case of adverse pressure gradient, for a large class of
boundary data at $x=0$.We justify the Goldstein singularity: more precisely, we
prove that under suitable assumptions on the boundary data at $x=0$, there
exists $x^*>0$ such that $\p\_y u\_{y=0}(x)\sim C \sqrt{x^* -x}$ as $x\to x^*$
for some positive constant $C$, where $u$ is the solution of the stationary
Prandtl equation in the domain $\{0<x<x^*,\ y>0\}$. Our proof relies on three
main ingredients: the computation of a "stable" approximate solution, using
modulation theory arguments, a new formulation of the Prandtl equation, for
which we derive energy estimates, relying heavily on the structure of the
equation, and maximum principle techniques to handle nonlinear terms.
