  A simple model to handle the flow of people in emergency evacuation
situations is considered: at every point x, the velocity U(x) that individuals
at x would like to realize is given. Yet, the incompressibility constraint
prevents this velocity field to be realized and the actual velocity is the
projection of the desired one onto the set of admissible velocities. Instead of
looking at a microscopic setting (where individuals are represented by rigid
discs), here the macroscopic approach is investigated, where the unknwon is the
evolution of the density . If a gradient structure is given, say U is the
opposite of the gradient of D where D is, for instance, the distance to the
exit door, the problem is presented as a Gradient Flow in the Wasserstein space
of probability measures. The functional which gives the Gradient Flow is
neither finitely valued (since it takes into account the constraints on the
density), nor geodesically convex, which requires for an ad-hoc study of the
convergence of a discrete scheme.
