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

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