Branching process associated with 2d-Navier Stokes equation
Saïd Benachour
Université Henri Poincaré, Vandoeuvre lès Nancy, FranceBernard Roynette
Université Henri Poincaré, Vandoeuvre lès Nancy, FrancePierre Vallois
Université Henri Poincaré, Vandoeuvre lès Nancy, France

Abstract
being a bounded open set in , with regular boundary, we associate with Navier-Stokes equation in where the velocity is null on ∂Ω, a non-linear branching process (). More precisely: E_{ω0} (h,Y_t) = (ω, h), for any test function , where ω = rot , denotes the velocity solution of Navier-Stokes equation. The support of the random measure 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