University of Cambridge > > Partial Differential Equations seminar > Propagation of chaos towards Navier-Stokes for stochastic system of 2D vortices

Propagation of chaos towards Navier-Stokes for stochastic system of 2D vortices

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We consider here a system of N vortices interacting between themselves via the Biot-Savard law, and driven by N independent Brownian motion. Osada showed in 1985 that if the viscosity is sufficiently strong, if the initial vorticity is bounded, then (full or trajectorial) propagation of chaos holds for that system, towards the expected non-linear SDE . In particular, the empirical measures associated to our vortices system converges in law towards the unique (under appropriate a priori assumptions) solution of the vorticity equation. After a short discussion about the interest of such model, we will present a result obtained in collaboration with Nicolas Fournier and Stéphane Mischler, which extends the result of Osada to any positive vorticity, any initial condition with finite entropy, and also provide a stronger convergence result: the propagation of chaos at fixed times is entropic. The proof also relies on very different arguments, that we shall present if time permits.

This talk is part of the Partial Differential Equations seminar series.

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