Abstract
The article is concerned with the problem of the unstability of flows corresponding to solutions of the Navier—Stokes equation in relation with the stability of a new functional equation (functional Navier—Stokes equation),that is stable as well as superstable in an extended Ulam sense. In such a framework a natural characterization of stable global laminar flows is given also.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.H. Hyers: On the stability of the linear functional equation’, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
A. Prâstaro: `Geometry of PDEs and Mechanics’, World Scientific Publ. Co., Singapore, 1996.
A. Prâstaro: `Quantum and integral (co)bordism groups in partial differential equations’, Acta Appl. Math. 51 (1998), 243–302. `Quantum and integral bordism groups in the Navier—Stokes equation’, pages 343–359 In: New Developments in Differential Geometry, Budapest 1996, J. Szenthe (ed.), Kluwer Academic Publishers, Dordrecht (1999). `(Co)bordism groups in PDEs’, Acta Appl. Math. 59 (2) (1999), 111–201.
A. Prâstaro, `Local and global solutions of the Navier—Stokes equation’, Steps in Differential Geometry, L. Kozman, P.T. Nagy and L. Tomassy (eds.), University of Debrecen, Hungary, 2001, 263–271.
A. Prâstaro: Navier—Stokes equation. Global existence and uniqueness’ (to appear)
Th.M. Rassias: `On the stability of the linear mapping in Banach spaces’, Proc. Amer. Math. Soc. 72 (1978), 297–300.
Th.M. Rassias: `On the stability of functional equations and a problem of Ulam’, Acta Appl. Math. 62 (2000), 23–130.
Th.M. Rassias: `On a modified Hyers—Ulam sequence’, J. Math. Anal. Appl. 158 (1991), 106–113.
Th.M. Rassias: `On a problem of S.M. Ulam and the asymptotic stability of the Cauchy functional equation with applications’, Intern. Ser. Numer. Math. 123 (1997), 297–309.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Prástaro, A., Rassias, T.M. (2003). On Ulam Stability in the Geometry of PDE’s. In: Rassias, T.M. (eds) Functional Equations, Inequalities and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0225-6_9
Download citation
DOI: https://doi.org/10.1007/978-94-017-0225-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6406-6
Online ISBN: 978-94-017-0225-6
eBook Packages: Springer Book Archive