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 a previous paper, 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.
Mean Field Limit of Interacting Filaments for 3D Euler Equations
Bessaih H.;Coghi M.;Flandoli F.
2019
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 a previous paper, 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.File in questo prodotto:
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