ULAM STABILITY IN GEOMETRY OF PDE'S

Abstract

The unstability of characteristic ows of solutions of PDEs is related to the Ulam stability of functional equations. In particular we consider as master equation the Navier-Stokes equation. The integral cobordism groups that have recently been introduced by APrastaro 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 ows associated to perturbed solutions of global laminar solutions of the Navier Stokes equation can be character ized by means of a stable as well superstable functional equation functional Navier Stokes equation. In such a framework a natural criterion to recognize stable laminar solutions is given.