, Volume 109, Issue 3, pp 343-366

Stochastic cascades and 3-dimensional Navier–Stokes equations

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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.

Received: 27 November 1996 / In revised form: 30 May 1997