Stochastic cascades and 3-dimensional Navier-Stokes equations. (English) Zbl 0888.60072

Le Jan, Y.; Sznitman, A. S.

Probab. Theory Relat. Fields 109, No. 3, 343-366 (1997).

Summary: We study the incompressible Navier-Stokes equations in \({\mathbb R}^3\). The nonlinear 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.

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
35Q30	Navier-Stokes equations

Keywords:

Navier-Stokes equations; Fourier transform; global existence and uniqueness