  We briefly report and elaborate on some conditions allowing a hydrodynamic
description of the impact of a very short and arbitrarily intense laser pulse
onto a cold plasma, as well as the localization of the first wave-breaking due
to the plasma inhomogeneity. We use a recently developed fully relativistic
plane model whereby we reduce the system of the Lorentz-Maxwell and continuity
PDEs into a 1-parameter family of decoupled systems of non-autonomous Hamilton
equations in dimension 1, with the light-like coordinate $\xi=ct\!-\!z$
replacing time $t$ as an independent variable. Apriori estimates on the
Jacobian $\hat J$ of the change from Lagrangian to Eulerian coordinates in
terms of the input data (initial density and pulse profile) are obtained
applying Liapunov direct method to an associated family of pairs of ODEs;
wave-breaking is pinpointed by the inequality $\hat J\le 0$. These results may
help in drastically simplifying the study of extreme acceleration mechanisms of
electrons, which have very important applications.
