Functional Analysis and Its Applications

, Volume 7, Issue 2, pp 137–146 | Cite as

Stability of plane-parallel Couette flow

  • V. A. Romanov


Functional Analysis Couette Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    C. C. Lin, Theory of Hydrodynamic Stability, Cambridge Univ. Press, Cambridge (1955).Google Scholar
  2. 2.
    O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, 2nd ed., Gordon and Breach (1968).Google Scholar
  3. 3.
    S. G. Krein, "Differential equations in Banach space and their application to hydromechanics," Usp. Matem. Nauk,12, No. 1, 208–210 (1957).Google Scholar
  4. 4.
    M. Z. Solomyak, "Application of semigroup theory to the study of differential equations in Banach spaces," Dokl. Akad. Nauk SSSR,122, No. 5, 766–769 (1958).Google Scholar
  5. 5.
    P. E. Sobolevskii, "Application of fractional powers of operators in the study of the Navier-Stokes equations," Dokl. Akad. Nauk SSSR,155, No. 1, 50–53 (1964).Google Scholar
  6. 6.
    V. I. Yudovich, "On the stability of stationary flows of a viscous incompressible liquid," Dokl. Akad. Nauk SSSR,161, No. 5, 1037–1040 (1965).Google Scholar
  7. 7.
    V. I. Yudovich, "On the stability of forced oscillations of a liquid," Dokl. Akad. Nauk SSSR,195, No. 2, 292–295 (1970).Google Scholar
  8. 8.
    S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, American Math. Soc. (1964).Google Scholar
  9. 9.
    S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967).Google Scholar
  10. 10.
    S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).Google Scholar
  11. 11.
    L. R. Volevich and B. P. Paneyakh, "Some spaces of generalized functions and imbedding theorems," Usp. Matem. Nauk,20, No. 1, 3–74 (1965).Google Scholar
  12. 12.
    L. Hopf, "Der Verlauf kleiner Schwingungen auf einer Strömung reibender Flüssigkeit," Ann. Phys.,44, 1–60 (1914).Google Scholar
  13. 13.
    W. Wasow, "On small disturbances of plane Couette flow," J. Res. Nat. Bur. Standards,51, 195–202 (1953).Google Scholar
  14. 14.
    D. Grohne, "Über das Spektrum bei Eigenschwingungen ebener Laminarströmungen," Z. angew. Math. und Mech.,34, 344–357 (1954).Google Scholar
  15. 15.
    A. P. Gallagher and A. Mc. D. Mercer, "On the behavior of small disturbances in plane Couette flow," J. Fluid Mech.,13, 91–100 (1962).Google Scholar
  16. 16.
    E. Riis, "The stability of Couette flow in non-stratified and stratified viscous fluids," Geophys. Publ.,23, 4, Oslo (1962).Google Scholar
  17. 17.
    L. A. Dikii, "On the stability of plane-parallel Couette flow," Prikl. Matem. i Mekh.,28, No. 2, 389–392 (1964).Google Scholar
  18. 18.
    R. V. Birikh, "On the spectrum of small disturbances of plane-parallel Couette flow," Prikl. Matem. i Mekh.,29, No. 4, 798–800 (1965).Google Scholar
  19. 19.
    Yu. B. Ponomarenko, "On the stability of plane Couette flow," Prikl. Matem. i Mekh.,32, No. 4, 606–614 (1968).Google Scholar
  20. 20.
    V. N. Shtern, "Stability of plane Couette flow," Zh. Prikl. Mekhan. i Tekh. Fiz.,5, 117–119 (1969).Google Scholar
  21. 21.
    D. D. Joseph, "Eigenvalue bounds for the Orr-Sommerfeld equation," J. Fluid Mech.,33, No. 3, 617–621 (1968).Google Scholar
  22. 22.
    W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley (1966).Google Scholar
  23. 23.
    E. Jahnke and F. Émde, Tables of Functions, Dover, New York (1945).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • V. A. Romanov

There are no affiliations available

Personalised recommendations