Lagrangian structures for the Stokes, Navier-Stokes and Euler equations

Jacky Cresson (1, 2) , Sébastien Darses (3)

1 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 Department of Mathematics and Statistics [Boston]

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]

Keywords: Lagrangian systems; Stochastic embedding; Navier-Stokes equations

Domains: Dynamical Systems [math.DS]; Probability [math.PR]; Analysis of PDEs [math.AP]

Jacky Cresson, Sébastien Darses. Lagrangian structures for the Stokes, Navier-Stokes and Euler equations. 2008. ⟨hal-00340120v1⟩