Regularized vortex approximation for 2D Euler equations with transport noise

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 $N$.

arXiv comment18 pages

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Cited by in corpus (2)

• Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise
• Hölder regularity for collapses of point vortices