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 = \mathrm{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
.