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Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus

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  • Cruzeiro, Ana Bela
  • Shamarova, Evelina

Abstract

We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier-Stokes equations in terms of diffusion processes.

Suggested Citation

  • Cruzeiro, Ana Bela & Shamarova, Evelina, 2009. "Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4034-4060, December.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:4034-4060
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    References listed on IDEAS

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    1. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
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    Cited by:

    1. Shamarova, Evelina & Sá Pereira, Rui, 2020. "Forward–backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3865-3894.
    2. Maurelli, Mario & Modin, Klas & Schmeding, Alexander, 2023. "Incompressible Euler equations with stochastic forcing: A geometric approach," Stochastic Processes and their Applications, Elsevier, vol. 159(C), pages 101-148.
    3. Delbaen, Freddy & Qiu, Jinniao & Tang, Shanjian, 2015. "Forward–backward stochastic differential systems associated to Navier–Stokes equations in the whole space," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2516-2561.

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