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A Hamiltonian Mean-Field System for the Navier-Stokes Equation

Mathematical Physics 2018-10-05 v2 math.MP

Abstract

We use a Hamiltonian interacting particle system to derive a stochastic mean field system whose McKean-Vlasov equation yields the incompressible Navier Stokes equation. Since the system is Hamiltonian, the particle relabeling symmetry implies a Kelvin Circulation Theorem along stochastic Lagrangian paths. Moreover, issues of energy dissipation are discussed and the model is connected to other approaches in the literature.

Keywords

Cite

@article{arxiv.1807.04123,
  title  = {A Hamiltonian Mean-Field System for the Navier-Stokes Equation},
  author = {Simon Hochgerner},
  journal= {arXiv preprint arXiv:1807.04123},
  year   = {2018}
}