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Stochastic cascades and 3-dimensional Navier–Stokes equations
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  • Published: November 1997

Stochastic cascades and 3-dimensional Navier–Stokes equations

  • Y. Le Jan1 &
  • A. S. Sznitman2 

Probability Theory and Related Fields volume 109, pages 343–366 (1997)Cite this article

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  • 66 Citations

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Summary.

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.

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris-Sud, Bat. 425, F-91405 Orsay Cedex, France, , , , , , FR

    Y. Le Jan

  2. Departement Mathematik, ETH-Zürich, CH-8092 Zürich, Switzerland, , , , , , CH

    A. S. Sznitman

Authors
  1. Y. Le Jan
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  2. A. S. Sznitman
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Received: 27 November 1996 / In revised form: 30 May 1997

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Jan, Y., Sznitman, A. Stochastic cascades and 3-dimensional Navier–Stokes equations. Probab Theory Relat Fields 109, 343–366 (1997). https://doi.org/10.1007/s004400050135

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  • Issue Date: November 1997

  • DOI: https://doi.org/10.1007/s004400050135

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  • AMS Subject Classification (1991): 60J80
  • 35Q30
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