scholarly journals Uniform Approximation of 2 Dimensional Navier--Stokes Equation by Stochastic Interacting Particle Systems

2020 ◽  
Vol 52 (6) ◽  
pp. 5339-5362
Author(s):  
Franco Flandoli ◽  
Christian Olivera ◽  
Marielle Simon
Keyword(s):  
Stokes Equation ◽  
Uniform Approximation ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Interacting Particle ◽  
Stochastic Interacting Particle Systems

scholarly journals Stochastic interacting particle systems out of equilibrium

2007 ◽  
Vol 2007 (07) ◽  
pp. P07014-P07014 ◽  
Author(s):  
L Bertini ◽  
A De Sole ◽  
D Gabrielli ◽  
G Jona-Lasinio ◽  
C Landim
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle ◽  
Stochastic Interacting Particle Systems

scholarly journals A Hamiltonian mean field system for the Navier–Stokes equation

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180178 ◽  
Author(s):  
Simon Hochgerner
Keyword(s):  
Energy Dissipation ◽  
Stokes Equation ◽  
Particle System ◽  
Mean Field ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Field System ◽  
Interacting Particle ◽  
Incompressible Navier Stokes Equation ◽  
Circulation Theorem

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.

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