Probability Theory and Related Fields

, Volume 121, Issue 3, pp 367–388

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

  • Sylvie Méléard

DOI: 10.1007/s004400100154

Cite this article as:
Méléard, S. Probab Theory Relat Fields (2001) 121: 367. doi:10.1007/s004400100154

Abstract.

We are interested in proving Monte-Carlo approximations for 2d Navier-Stokes equations with initial data u0 belonging to the Lorentz space L2,∞ and such that curl u0 is a finite measure. Giga, Miyakawaand Osada [7] proved that a solution u exists and that u=K* curl u, where K is the Biot-Savartkernel and v = curl u is solution of a nonlinear equation in dimension one, called the vortex equation.

In this paper, we approximate a solution v of this vortex equationby a stochastic interacting particlesystem and deduce a Monte-Carlo approximation for a solution of the Navier-Stokesequation. That gives in this case a pathwise proofof the vortex algorithm introducedby Chorin and consequently generalizes the works ofMarchioro-Pulvirenti [12] and Méléardv [15] obtained in the case of a vortex equation with bounded density initial data.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sylvie Méléard
    • 1
  1. 1.Université Paris 10, MODALX, 200 avenue de la République, 92000 Nanterre France e-mail: sylm@ccr.jussieu.frFR