An elementary proof of the existence and uniqueness theorem for the Navier-Stokes equations

Communications in Contemporary Mathematics

Volumn 1, Issue 4, 1999, Pages 497-516

  Mattingly, J C ^a   Sinai, Ya G ^b  

^a STANFORD UNIVERSITY   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844453762     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199799000183     Document Type: Article

References (13)

1. P. Constantin and C. Foiaş, Navier-Stokes Equations, University of Chicago Press, Chicago (1988).
2. A. J. Chorin and J. E. Marsden, A mathematical introduction to fluid mechanics, Vol. 4, Texts in Applied Mathematics, Springer-Verlag, New York, third edition (1993).
3. C. R. Doering and J. D. Gibbon, Applied analysis of the Navier-Stokes equations, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (1995).
4. C. R. Doering and E. S. Titi, Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations, Phys. Fluids 7 (1995) 1384-1390.
5. C. Foiaş and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal. 87 (1989) 359-369.
6. G. Gallavotti, Ipotesi per una introduzione alla Meccanica Dei Fluidi, Gruppo Nazionale Di Fisica Matematica, 1996.
7. E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr. 4 (1951) 213-231.
8. Heinz-Otto Kreiss, Fourier expansions of the solutions of the Navier-Stokes equations and their exponential decay rate, In Analyse mathématique et applications, Gauthier-Villars, Paris (1988), pp. 245-262.
9. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York (1969).
10. J. Leray, Essai sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934) 193-248.
11. R. Temam, Navier-Stokes equations: Theory and numerical analysis, Vol. 2 of Studies in Mathematics and its Applications, North-Holland Publishing Co., Amsterdam-New York, revised edition (1979).
12. R. Temam, Navier-Stokes equations and nonlinear functional analysis, Vol. 66 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition (1995).
13. V. I. Yudovich, The linearization method in hydrodynamical stability theory, American Mathematical Society, Providence, RI, 1989. Translated from the Russian by J. R. Schulenberger.