Resumen de Branching process associated with 2d-Navier Stokes equation

Pierre Vallois, Said Benachour, Bernard Roynette

• O being a bounded open set in R·, with regular boundary, we associate with Navier-Stokes equation in O where the velocity is null on ?O, a non-linear branching process (Yt, t = 0). More precisely: E?0(áh,Ytñ) = á?,hñ, for any test function h, where ? = rot u, u denotes the velocity solution of Navier-Stokes equation. The support of the random measure Yt increases or decreases in one unit when the underlying process hits ?O; this stochastic phenomenon corresponds to the creation-annihilation of vortex localized at the boundary of O.