Symmetries and Martingales in a Stochastic Model for the Navier-Stokes Equation

  • Rémi Lassalle
  • Ana Bela CruzeiroEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 162)


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.


Stochastic analysis Stochastic control Navier-Stokes equation 

Mathematics Subject Classification:

93E20 60H30 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.CEREMADE, Université Paris-DauphineParisFrance
  2. 2.GFMUL and Departamento Matemática Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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