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arXiv · 1912.07233

Regularized vortex approximation for 2D Euler equations with transport noise

Michele Coghi·Mario Maurelli
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Abstract

We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot-Savart kernel and the same common noise. The approximation happens by sending the number of particles $N$ to infinity and the regularization $\epsilon$ in the Biot-Savart kernel to $0$, as a suitable function of $N$.

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Michele Coghi, Mario Maurelli. 2019-12-16. Regularized vortex approximation for 2D Euler equations with transport noise. https://doi.org/10.1142/s021949372040002x

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