Mean field limit of interacting filaments for 3D Euler equations

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.

19 pages

References in corpus (1)

• Mean field limit of interacting filaments and vector valued non linear PDEs

Cited by in corpus (3)

• Pathwise McKean-Vlasov Theory with Additive Noise
• A Central Limit Theorem for Gibbsian Invariant Measures of 2D Euler Equations
• Regularized vortex approximation for 2D Euler equations with transport noise