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

2008/11/20 by Jacky Cresson, Cresson, Jacky, Sébastien Darses +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0811.3286

openalex publication_date 2008/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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]

Citations

• Dynamical Theories of Brownian Motion

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