The unstability of characteristic flows of solutions of PDE's is related to the Ulam stability of functional equations. In particular, we consider, as master equation, the Navier-Stokes equation. The integral (co)bordism groups, that have recently been introduced by A. Pr\'astaro to solve the problem of existence of global solutions of the Navier-Stokes equation, lead to a new application of the Ulam stability for functional equations. This allowed us here to prove that the characteristic flows associated to perturbed solutions of global laminar solutions of the Navier-Stokes equation, can be characterized by means of a stable (as well superstable) functional equation (\textit{functional Navier-stokes equation}). In such a framework a natural criterion to recognize stable laminar solutions is given also.
Ulam stability in geometry of PDE's / Prastaro, Agostino; Rassias, T. H. M.. - In: NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS. - ISSN 1229-1595. - STAMPA. - 2:8(2003), pp. 259-278.
Ulam stability in geometry of PDE's
PRASTARO, Agostino;
2003
Abstract
The unstability of characteristic flows of solutions of PDE's is related to the Ulam stability of functional equations. In particular, we consider, as master equation, the Navier-Stokes equation. The integral (co)bordism groups, that have recently been introduced by A. Pr\'astaro to solve the problem of existence of global solutions of the Navier-Stokes equation, lead to a new application of the Ulam stability for functional equations. This allowed us here to prove that the characteristic flows associated to perturbed solutions of global laminar solutions of the Navier-Stokes equation, can be characterized by means of a stable (as well superstable) functional equation (\textit{functional Navier-stokes equation}). In such a framework a natural criterion to recognize stable laminar solutions is given also.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.