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
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 $(NS)$.
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/174181
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact