Geodesic
Propagation of chaos for the 2D viscous vortex model
Journal of the European Mathematical Society, Tome 16 (2014) no. 7, pp. 1423-1466 Cet article a éte moissonné depuis la source EMS Press

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We consider a stochastic system of N particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly stronger result: the propagation of chaos of the stochastic paths towards the solution of the expected nonlinear stochastic differential equation. Moreover, the convergence holds in a strong sense, usually called entropic (there is no loss of entropy in the limit). The result holds without restriction (but positivity) on the viscosity parameter.
DOI : 10.4171/jems/465
Classification : 65-XX, 35-XX, 82-XX
Keywords: 2D Navier-Stokes equation, Stochastic particle systems, Propagation of Chaos, Fisher information, Entropy dissipation 
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     author = {Nicolas Fournier and Maxime Hauray and St\'ephane Mischler},
     title = {Propagation of chaos for the {2D} viscous vortex model},
     journal = {Journal of the European Mathematical Society},
     pages = {1423--1466},
     year = {2014},
     volume = {16},
     number = {7},
     doi = {10.4171/jems/465},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/465/}
}
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Nicolas Fournier; Maxime Hauray; Stéphane Mischler. Propagation of chaos for the 2D viscous vortex model. Journal of the European Mathematical Society, Tome 16 (2014) no. 7, pp. 1423-1466. doi: 10.4171/jems/465

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