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

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.

References in corpus (4)

• Solution properties of a 3D stochastic Euler fluid equation
• Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
• Stochastic mean-field approach to fluid dynamics
• A Stochastic Lagrangian particle system for the Navier-Stokes equations

Cited by in corpus (4)

• A canonical Hamiltonian formulation of the Navier-Stokes problem
• Lagrangian averaged stochastic advection by Lie transport for fluids
• A Hamiltonian interacting particle system for compressible flow
• Probabilistic representation of helicity in viscous fluids