Reversal in the Stationary Prandtl Equations

We discuss a recent result in which we investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by spatio-temporal regions in which $u > 0$ and $u < 0$. The classical point of view of regarding the Prandtl equations as an evolution $x$ completely breaks down. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. Joint work with Nader Masmoudi.