In the geometric formal theory of PDE's we recognize also the problem of existence of singular solutions with singularities of Thom-Boardman type, i.e., singularities that can be resolved by means of prolongations. Scope of this paper is to give a short account of some fundamental results in these directions and apply them to some important classic equations of fluid mechanics: Euler equation $(E)$ and Navier-Stokes equation $(NS)$. Quantum tunneling effects can be described by means of such singular solutions. Furthermore, we show also as singular solutions enter in the description of canonical quantization of PDE's. We shall specialize, for sake of coincision, on equations $(E)$ and $(NS)$.