# Branching process associated with 2d-Navier Stokes equation

### Saïd Benachour

Université Henri Poincaré, Vandoeuvre lès Nancy, France### Bernard Roynette

Université Henri Poincaré, Vandoeuvre lès Nancy, France### Pierre Vallois

Université Henri Poincaré, Vandoeuvre lès Nancy, France

## Abstract

$\Omega$ being a bounded open set in $\mathbb R^2$, with regular boundary, we associate with Navier-Stokes equation in $\Omega$ where the velocity is null on ∂Ω, a non-linear branching process ($Y_t; t ≥ 0$). More precisely: E_{ω0} (h,Y_t) = (ω, h), for any test function $h$, where ω = rot $u$, $u$ denotes the velocity solution of Navier-Stokes equation. The support of the random measure $Y_t$ increases or decreases of one unit when the underlying process hits ∂Ω; this stochastic phenomenon corresponds to the creation-annihilation of vortex localized at the boundary of Ω.

## Cite this article

Saïd Benachour, Bernard Roynette, Pierre Vallois, Branching process associated with 2d-Navier Stokes equation. Rev. Mat. Iberoam. 17 (2001), no. 2, pp. 331–373

DOI 10.4171/RMI/297