Ulam stability in geometry of PDE's
Ulam stability in geometry of PDE's
The concept of Hyers-Ulam-Rassias stability is applied to the Navier-Stokes equation. In the first part of the paper the geometric formulation of the Navier-Stokes equation as introduced by A.~Prástaro is recalled. The second part contains a~short account on the stability of functional equations. An extension of this concept, suitable to be applied to the Navier-Stokes equation, is given. In the main part of the paper the instability of a~solution of the Navier-Stokes equation is related to the stability of a~functional equation describing the time evolutions of the characteristic vector fields of solutions.
Navier-Stokes equations for incompressible viscous fluids, functional equations, integral (co)bordism groups, Ulam stability; Stability in PDE's geometry; Applications., Stability, separation, extension, and related topics for functional equations, Hyers-Ulam-Rassias stability, Navier-Stokes equations, Navier-Stokes equation
Navier-Stokes equations for incompressible viscous fluids, functional equations, integral (co)bordism groups, Ulam stability; Stability in PDE's geometry; Applications., Stability, separation, extension, and related topics for functional equations, Hyers-Ulam-Rassias stability, Navier-Stokes equations, Navier-Stokes equation
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