  We study the interaction between the stability, and the propagation of
regularity, for solutions to the incompressible 3D Euler equation. It is still
unknown whether a solution with smooth initial data can develop a singularity
in finite time. This article explains why the prediction of such a blow-up, via
direct numerical experiments, is so difficult. It is described how, in such a
scenario, the solution becomes unstable as time approaches the blow-up time.
