JournalsrmiVol. 17, No. 2pp. 331–373

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
Branching process associated with 2d-Navier Stokes equation cover

Abstract

Ω\Omega being a bounded open set in R2\mathbb R^2, with regular boundary, we associate with Navier-Stokes equation in Ω\Omega where the velocity is null on ∂Ω, a non-linear branching process (Yt;t0Y_t; t ≥ 0). More precisely: E_{ω0} (h,Y_t) = (ω, h), for any test function hh, where ω = rot uu, uu denotes the velocity solution of Navier-Stokes equation. The support of the random measure YtY_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