  To date it has not been possible to prove whether or not the
three-dimensional incompressible Euler equations develop singular behaviour in
finite time. Some possible singular scenarios, as for instance shock-waves, are
very important from a physical point of view, since they imply the connection
among the macroscopic and the microscopic scale. Therefore, the appearence of
this type of singularity or a similar one might be interpreted as a possible
explanation of the transition to turbulence. In order to clarify the question,
some one-dimensional models for ideal incompressible hydrodynamics have been
introduced and analyzed, and it was proven that shock-waves appear in finite
time within this type of flow. In this work we question the validity of these
models and analyze the physical meaning that the occurrence of a singularity in
an incompressible flow, if it happens, may have.
