Communications in Mathematical Physics

, Volume 90, Issue 2, pp 187–206 | Cite as

Self-similar universal homogeneous statistical solutions of the Navier-Stokes equations

  • C. Foias
  • R. Temam


In this note we consider a family of statistical solutions of the Navier-Stokes equations (i.e. time dependent solutions of the Hopf equation) which seem to constitute the rigorous mathematical framework for the theory of homogeneous turbulence [1], [13]. The main feature of these solutions is that they are the transforms under suitable scalings of thestationary statistical solutions of a new system of equations (the Eq. (2) below).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Statistical Solution 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • C. Foias
    • 1
  • R. Temam
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Laboratoire d'Analyse Numérique, Batiment 425Université Paris-SudOrsayFrance

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