  The present understanding of supernova explosion of massive stars as a
two-step process, with an initial gravitational collapse toward the center of
the star followed by an expansion of matter after a bouncing on the core, meets
several difficulties. We show that it is not the only possible one: a simple
model based on fluid mechanics, catastrophe theory, and stability properties of
the equilibrium state shows that one can have also a simultaneous
inward/outward motion in the early stage of the instability of the supernova
described by a dynamical saddle-center bifurcation. The existence of this
simultaneous inward/outward motion is sensitive to the model in such systems
with long-range interactions. If a constant temperature is assumed (canonical
ensemble), an overall inward motion occurs, but if one imposes with the same
equation of state the constraint of energy conservation (microcanonical
ensemble) there is an inward velocity field near the center of the star
together with an outward velocity field in the rest of the star. We discuss the
expansion stage of the remnants away from the collapsed core, and propose a new
explanation for the formation of shock waves in the ejecta which differs from
the usual Sedov-Taylor self-similar description.
