Stochastic Mean-Field Approach to Fluid Dynamics
@article{Hochgerner2017StochasticMA, title={Stochastic Mean-Field Approach to Fluid Dynamics}, author={Simon Hochgerner}, journal={Journal of Nonlinear Science}, year={2017}, volume={28}, pages={725-737} }
It is shown that the incompressible Navier–Stokes equation can be derived from an infinite-dimensional mean-field stochastic differential equation.
4 Citations
A Hamiltonian mean field system for the Navier–Stokes equation
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The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system…
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References
SHOWING 1-10 OF 27 REFERENCES
A mathematical introduction to fluid mechanics
- Mathematics
- 1979
Contents: The Equations of Motion.- Potential Flow and Slightly Viscous Flow.- Gas Flow in One Dimension.- Vector Identities.- Index.
An Eulerian-Lagrangian approach for incompressible fluids: Local theory
- Mathematics
- 2000
We study a formulation of the incompressible Euler equations in terms of the inverse Lagrangian map. In this formulation the equations become a first order advective nonlinear system of partial…
Hydrodynamics, Probability and the Geometry of the Diffeomorphisms Group
- Mathematics
- 2011
We characterize the solution of Navier-Stokes equation as a stochastic geodesic on the diffeomorphisms group, thus generalizing Arnold’s description of the Euler flow.
Solution Properties of a 3D Stochastic Euler Fluid Equation
- MathematicsJ. Nonlinear Sci.
- 2019
We prove local well-posedness in regular spaces and a Beale–Kato–Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model…
Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus
- Mathematics
- 2008
Navier-Stokes Equation and Diffusions on the Group of Homeomorphisms of the Torus
- Mathematics
- 2007
A stochastic variational principle for the (two dimensional) Navier-Stokes equation is established. The velocity field can be considered as a generalized velocity of a diffusion process with values…
A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations
- Mathematics
- 2005
In this paper we derive a probabilistic representation of the deterministic three‐dimensional Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven…
A Stochastic Perturbation of Inviscid Flows
- Mathematics
- 2006
AbstractWe prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and…
Groups of diffeomorphisms and the motion of an incompressible fluid
- Mathematics
- 1970
In this paper we are concerned with the manifold structure of certain groups of diffeomorphisms, and with the use of this structure to obtain sharp existence and uniqueness theorems for the classical…