Symmetries and martingales in a stochastic model for the Navier-Stokes equation

2016/02/11 by Ana Bela Cruzeiro, Cruzeiro, Ana Bela, Rémi Lassalle +1
Economics, Econometrics and Finance · Engineering · Mathematics · #60H30 #93E20 #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1602.03657

openalex publication_date 2016/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A stochastic description of solutions of the Navier-Stokes equation is investigated. These solutions are represented by laws of finite dimensional semi-martingales and characterized by a weak Euler- Lagrange condition. A least action principle, related to the relative entropy, is provided. Within this stochastic framework, by assuming further symmetries, the corresponding invariances are expressed by martingales, stemming from a weak Noether's theorem.

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