Monte-Carlo approximations for 2d Navier-Stokes equations with measure initial data

We are interested in proving Monte-Carlo approximations for 2d Navier-Stoke s equations with initial data u(o) belonging to the Lorentz space L-2,L-inf inity and such that curl u(o) is a finite measure. Giga, Miyakawa and Osada [7] proved that a solution it exists and that u = K-* curl u, where K is t he Biot-Savart kernel and v = curl it is solution of a nonlinear equation i n dimension one, called the vortex equation. In this paper, we approximate a solution v of this vortex equation by a sto chastic interacting particle system and deduce a Monte-Carlo approximation for a solution of the Navier-Stokes equation. That gives in this case a pat hwise proof of the vortex algorithm introduced by Chorin and consequently g eneralizes the works of Marchioro-Pulvirenti [12] and Meleard [15] obtained in the case of a vortex equation with bounded density initial data.