Mean Field Limit of Interacting Filaments for 3D Euler Equations

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