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

DOI: 10.1007/s004400050135

Cite this article as:
Jan, Y. & Sznitman, A. Probab Theory Relat Fields (1997) 109: 343. doi:10.1007/s004400050135


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): 60J8035Q30

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