Probability Theory and Related Fields

, Volume 109, Issue 3, pp 343–366

Stochastic cascades and 3-dimensional Navier–Stokes equations

  • Y. Le Jan
  • A. S. Sznitman


In this article, we study the incompressible Navier–Stokes equations in ℝ3. The non linear integral equation satisfied by the Fourier transform of the Laplacian of the velocity field can be interpreted in terms of a branching process and a composition rule along the associated tree. We derive from this representation new classes where global existence and uniqueness can be proven.

AMS Subject Classification (1991): 60J80 35Q30 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Y. Le Jan
    • 1
  • A. S. Sznitman
    • 2
  1. 1.Département de Mathématiques, Université Paris-Sud, Bat. 425, F-91405 Orsay Cedex, FranceFR
  2. 2.Departement Mathematik, ETH-Zürich, CH-8092 Zürich, SwitzerlandCH

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