  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.
