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November 2000 A trajectorial proof of the vortex method for the two-dimensional Navier-Stokes equation
Sylvie Méléard
Ann. Appl. Probab. 10(4): 1197-1211 (November 2000). DOI: 10.1214/aoap/1019487613


We consider the Navier–Stokes equation in dimension 2 and more precisely the vortex equation satisfied by the curl of the velocity field.We show the relation between this equation and a nonlinear stochastic differential equation. Next we use this probabilistic interpretation to construct approximating interacting particle systems which satisfy a propagation of chaos property: the laws of the empirical measures tend, as the number of particles tends to $\infty$, to a deterministic law for which marginals are solutions of the vortex equation.This pathwise result justifies completely the vortex method introduced by Chorin to simulate the solutions of the vortex equation.Our approach is inspired by Marchioro and Pulvirenti and we improve their results in a pathwise sense.


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Sylvie Méléard. "A trajectorial proof of the vortex method for the two-dimensional Navier-Stokes equation." Ann. Appl. Probab. 10 (4) 1197 - 1211, November 2000.


Published: November 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1073.76543
MathSciNet: MR1810871
Digital Object Identifier: 10.1214/aoap/1019487613

Primary: 60K35
Secondary: 76D05

Keywords: interacting particle systems , propogation of chaos , Two-dimensional Navier-Stokes equation , vortex method

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 4 • November 2000
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