Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A note on the exstencie of periodic solutions of the Navier-Stokes equations

This is a preview of subscription content, log in to check access.


  1. [1]

    Serrin, J.: On the stability of viscous fluid motions. Arch. Rational Mech. Anal. 3, 1–13 (1959).

  2. [2]

    Leray, J.: Étude de diverses équations intégrales nonlinéares et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl. (9) 12, 1–82 (1933).

  3. [3]

    Leray, J.: Essai sur les mouvements plan d'un liquide visqueux que limitent des parois. J. Math. Pures Appl. (9) 13, 331–418 (1934).

  4. [4]

    Leray, J.: Sur le mouvement d'un liquide visqueux remplissant l'espace. Acta Math. 63, 193–248 (1934).

  5. [5]

    Kiselev, A. A., & O. A. Ladyshenskaya: On the existence and uniqueness of solutions of the initial value problem for viscous incompressible fluids. Izvestia Akad. Nauk SSSR. 21, 655–670 (1957).

Download references

Author information

Additional information

This research was supported in part by the United States Air Force Office of Scientific Research under Contract AF 49 (638)-262.

Communicated by C. Truesdell

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Serrin, J. A note on the exstencie of periodic solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 3, 120–122 (1959).

Download citation


  • Neural Network
  • Complex System
  • Periodic Solution
  • Nonlinear Dynamics
  • Electromagnetism