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Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems

Abstract : We consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-Stokes equation written in vorticity form. The proofs follow a semigroup approach.
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Submitted on : Friday, October 16, 2020 - 9:28:13 AM
Last modification on : Thursday, April 29, 2021 - 3:26:02 PM

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Franco Flandoli, Christian Olivera, Marielle Simon. Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), ⟨10.1137/20M1328993⟩. ⟨hal-02529632v2⟩

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