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 $(NS)$.
On the singular solutions of PDE's / Prastaro, Agostino. - STAMPA. - (1990), pp. 17-20. (Intervento presentato al convegno X Congresso Nazionale AIMETA tenutosi a Pisa nel 1990).
On the singular solutions of PDE's.
PRASTARO, Agostino
1990
Abstract
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 $(NS)$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.