  We discuss a Lagrangian reconstruction method of the velocity field from
galaxy redshift catalog that takes its root in the Euler equation. This results
in a ``functional'' of the velocity field which must be minimized. This is
helped by an algorithm solving the minimization of cost-flow problems. The
results obtained by applying this method to cosmological problems are shown and
boundary effects happening in real observational cases are then discussed.
Finally, a statistical model of the errors made by the reconstruction method is
proposed.
