Lagrangian structures for the Stokes, Navier-Stokes and Euler equations
Analysis of PDEs
2008-11-21 v1 Dynamical Systems
Probability
Abstract
We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [Cresson-Darses, J. Math. Phys. 48, 072703 (2007]
Cite
@article{arxiv.0811.3286,
title = {Lagrangian structures for the Stokes, Navier-Stokes and Euler equations},
author = {Jacky Cresson and Sébastien Darses},
journal= {arXiv preprint arXiv:0811.3286},
year = {2008}
}