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arXiv · 1711.01414

Mean field limit of interacting filaments for 3D Euler equations

Hakima Bessaih·Michele Coghi·Franco Flandoli
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Abstract

The 3D Euler equations, precisely local smooth solutions of class $H^s$ with $s>5/2$, are obtained as a mean field limit of finite families of interacting curves, the so called vortex filaments, described by means of the concept of $1$-currents. This work is a continuation of the a previous work, where a preliminary result in this direction was obtained, with the true Euler equations replaced by a vector valued non linear PDE with a mollified Biot-Savart relation.

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Hakima Bessaih, Michele Coghi, Franco Flandoli. 2017-11-04. Mean field limit of interacting filaments for 3D Euler equations. https://doi.org/10.1007/s10955-018-2189-4

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