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}
}