Communications in Mathematical Physics

, Volume 105, Issue 1, pp 99–106 | Cite as

An example of absence of turbulence for any Reynolds number

  • Carlo Marchioro


We consider a viscous incompressible fluid moving in a two-dimensional flat torus. We show a particular external forcef0 for which there is a globally attractive stationary state for any Reynolds numberR. Moreover, for any fixedR, this stability property holds also for a neighbourhood off0.


Neural Network Statistical Physic Reynolds Number Complex System Stationary State 
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  1. 1.
    Joseph, D.D.: Stability of fluid motion. Vol. I, II. Berlin, Heidelberg, New York: Springer 1976Google Scholar
  2. 2.
    Boldrighini, C., Franceschini, V.: A five-dimensional truncation of the plane incompressible Navier-Stokes equations. Commun. Math. Phys.64, 159 (1979)Google Scholar
  3. 2a.
    Franceschini, V., Tebaldi, C.: Sequences of infinite bifurcations and turbulence in a five model truncation of the Navier-Stokes equations. J. Stat. Phys.21, 707 (1979)Google Scholar
  4. 2b.
    Franceschini, V., Tebaldi, C.: A seven model truncation of the plane incompressible Navier-Stokes equations. J. Stat. Phys.25, 397 (1981)Google Scholar
  5. 2c.
    Riela, G.: A new six mode truncation of Navier-Stokes equation on a two dimensional torus: a numerical study. Nuovo Cimento69B, 245 (1982)Google Scholar
  6. 2d.
    Franceschini, V., Tebaldi, C., Zironi, F.: Fixed point behaviour ofN mode truncated Navier-Stokes equations asN increases. J. Stat. Phys.35, 387 (1984)Google Scholar
  7. 2e.
    Franceschini, V., Tebaldi, C.: Truncation to 12, 14, and 18 modes of the Navier-Stokes equations on a two dimensional torus. Meccanica (in press)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Carlo Marchioro
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma I “La Sapienza”RomaItaly

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