Journal of Statistical Physics

, Volume 174, Issue 3, pp 562–578

Mean Field Limit of Interacting Filaments for 3D Euler Equations

• Hakima Bessaih
• Michele Coghi
• Franco Flandoli
Article

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.

Keywords

3D Euler equations Vortex filaments Currents Mean field theory

Mathematics Subject Classification

Primary 35Q31 70F45 Secondary 37C10 76B47 49Q15

Notes

Acknowledgements

We would like to thank the anonymous referees for their careful reading and valuable remarks which helped improving this paper. Hakima Bessaih’s research was partially supported by NSF Grant DMS-1418838. Franco Flandoli was partially supported by the PRIN 2015 project “Deterministic and stochastic evolution equations”.

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Authors and Affiliations

• Hakima Bessaih
• 1
Email author
• Michele Coghi
• 2
• Franco Flandoli
• 3
1. 1.Department of Mathematics and StatisticsUniversity of WyomingLaramieUnited States
2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
3. 3.Scuola Normale SuperiorePisaItaly